<Text-field style="Heading 1" layout="Heading 1">Problem 8-6</Text-field>

Green's Second Identity

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

Using the functions 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 and 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, verify Green's second identity

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 = 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

where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= are the interior and surface of a unit sphere centered at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY3RjBGNEY0RjQ=.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

<Text-field style="Heading 1" layout="Heading 1">Solution (Maple 14)</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Data Entry</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

Control-drag the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSkmaGVsbGlwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xNjY2NjY3ZW1GJy9GTkZTRjk=

Context Menu: Assign Name

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=

assign( );

Control-drag the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSkmaGVsbGlwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xNjY2NjY3ZW1GJy9GTkZTRjk=

Context Menu: Assign Name

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=

assign( );

Set the coordinate system

Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Vector Algebra and Settings\342\211\273Set Coordinates\342\211\273The More Common Systems

The More Common Coordinate Systems

Cartesian [x\134,y],Cartesian [x\134,y\134,z],Cartesian - other,polar,cylindrical,sphericaluse DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local q; Do(q = %ComboBox2): if q=Cartesian [x,y] then Do(%MathContainer22=MathML[Export]([x,y])); elif q=Cartesian [x,y,z] then Do(%MathContainer22=MathML[Export]([x,y,z])); elif q=Cartesian - other then Do(%MathContainer22=NULL); elif q=polar then Do(%MathContainer22=NULL); elif q=cylindrical then Do(%MathContainer22=NULL); elif q=spherical then Do(%MathContainer22=NULL); end if: Do(%MathContainer23 = NULL); end module; end use;

use DocumentTools,VectorCalculus in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local q,q1,q2,q3; Do(q = %ComboBox2); if q<>Cartesian [x,y] and q<> Cartesian [x,y,z] then Do(q1 = %MathContainer22); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; end if; if q=Cartesian [x,y] then SetCoordinates(cartesian[x,y]); elif q=Cartesian [x,y,z] then SetCoordinates(cartesian[x,y,z]); elif q=Cartesian - other then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["cartesian",convert(q2,string)],""))) else return;end if; elif q=polar then if nops(q2)=2 then SetCoordinates(parse(StringTools:-Join(["polar",convert(q2,string)],""))) else return;end if; elif q=cylindrical then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["cylindrical",convert(q2,string)],""))) else return;end if; elif q=spherical then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["spherical",convert(q2,string)],""))) else return;end if; end if; q3 := GetCoordinates(); Do(%MathContainer23 = MathML[Export]([op(0,q3),[op(q3)]])); end module; end use;

<Text-field style="Heading 2" layout="Heading 2">Volume Integral</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

Implement the volume integral 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

Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Integration\342\211\273Multiple Integration\342\211\2733-D\342\211\273Over a Sphere

Integrate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= over a Sphere

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

use DocumentTools in Do(%MathContainer24 = NULL); end use;

Center LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJiRidGNEY3RjotRjE2JVEiY0YnRjRGN0Y+Rj4tRjE2I1EhRidGPg==: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer25 = NULL); Do(%MathContainer26 = NULL); Do(%MathContainer27 = NULL); end use; Radius =

use DocumentTools in Do(%MathContainer28 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools,VectorCalculus in module() local f, a,b,c, R, q; Do(f = %MathContainer24); Do(a = %MathContainer25); Do(b = %MathContainer26); Do(c = %MathContainer27); Do(R = %MathContainer28); if nops([f])*nops([a])*nops([b])*nops([c])*nops([R])=0 then return;end if; q := int(f,[x,y,z]=Sphere(<a,b,c>,R,[rho,phi,theta]),inert); Do(%MathContainer29 = q); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUScmIzk1MjtGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSJ+RidGOi8lJmZlbmNlR0Y5LyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlBGKy1GLDYlUScmIzk2NjtGJ0Y4RjpGPEYrLUYsNiVRJyYjOTYxO0YnRjhGOkY6

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in module() local q; Do(q = %MathContainer30); if nops([q])=0 then return;end if; Do(%MathContainer30 = simplify(q)); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer30); Do(%MathContainer30 = evalf(q)); end module; end use;

use DocumentTools in Do(%MathContainer24 = NULL); Do(%MathContainer25 = NULL); Do(%MathContainer26 = NULL); Do(%MathContainer27 = NULL); Do(%MathContainer28 = NULL); Do(%MathContainer29 = NULL); Do(%MathContainer30 = NULL); end use;

<Text-field style="Heading 2" layout="Heading 2">Flux Integral</Text-field>

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Implement the flux integral 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

Type 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

Context Menu: Assign to a Name\342\211\273F

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Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Integration\342\211\273Flux\342\211\2733-D\342\211\273Through a Sphere

Flux through a Sphere

For the Vector Field:

use DocumentTools in Do(%ComboBox3(value) = "Select Coordinate System"): Do(%MathContainer31 = NULL); Do(%MathContainer32 = NULL); Do(%MathContainer33 = NULL); Do(%MathContainer34 = NULL); Do(%MathContainer35 = NULL); Do(%MathContainer40 = NULL); Do(%MathContainer41 = NULL); Do(%MathContainer36 = NULL); Do(%MathContainer37 = NULL); Do(%MathContainer38 = NULL); Do(%MathContainer39 = NULL); Do(%MathContainer31(visible) = false); Do(%MathContainer32(visible) = false); Do(%MathContainer33(visible) = false); Do(%MathContainer34(visible) = false); Do(%MathContainer35(visible) = false); Do(%MathContainer40(visible) = false); Do(%MathContainer41(visible) = false); Do(%MathContainer36(visible) = false); Do(%MathContainer37(visible) = false); Do(%MathContainer38(visible) = false); Do(%MathContainer39(visible) = false); Do(%Label13(visible) = false); Do(%Label14(visible) = false); Do(%Label15(visible) = false); Do(%Label16(visible) = false); Do(%Label17(visible) = false); Do(%Label18(visible) = false); Do(%Label19(visible) = false); Do(%Label20(visible) = false); Do(%Label21(visible) = false); Do(%Button34(visible) = false); Do(%Button35(visible) = false); Do(%Button37(visible) = false); Do(%Button38(visible) = false); Do(%Button36(visible) = false); Do(%Button42(enabled) = false); Do(%Button43(enabled) = false); Do(%Button44(enabled) = false); Do(%Button45(enabled) = false); Do(%Button46(enabled) = false); Do(%Button39(visible) = false); Do(%Button40(visible) = false); Do(%Button41(visible) = false); Do(%RadioButton0(visible) = false); Do(%RadioButton1(visible) = false); end use;

Select Coordinate System,Cartesian [x\134,y\134,z],Cartesian - other,cylindrical,spherical,bipolarcylindrical,bispherical,cardioidal,cardioidcylindrical,casscylindrical,conical,ellcylindrical,hypercylindrical,invcasscylindrical,logcylindrical,logcoshcylindrical,oblatespheroidal,paraboloidal,paracylindrical,prolatespheroidal,rosecylindrical,sixsphere,tangentcylindrical,tangentsphere,toroidaluse DocumentTools in module() local q; if GetProperty(ComboBox3,value) = "Select Coordinate System" then Do(%Label13(Visible) = false); Do(%MathContainer31 =NULL); Do(%MathContainer31(visible) = false); Do(%Button34(visible) = false); Do(%MathContainer32 = NULL); Do(%MathContainer32(visible) = false); return;end if; Do(q = %ComboBox3); if q=Cartesian [x,y,z] then Do(%MathContainer31=MathML[Export]([x,y,z])); elif q=Cartesian - other then Do(%MathContainer31 = NULL); else Do(%MathContainer31 = NULL); end if: Do(%MathContainer32 = NULL); Do(%Label13(visible) = true); Do(%MathContainer31(visible) = true); Do(%Button34(visible) = true); Do(%MathContainer32(visible) = true); #Do(%MathContainer34 = NULL); #Do(%MathContainer35 = NULL); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools, StringTools in xxxVFconstruct := module() local q,q1,q2; export q3; Do(q = %ComboBox3); Do(q1 = %MathContainer31); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if q=Cartesian [x,y,z] then q3 := parse(Join(["cartesian",convert(q2,string)],"")); elif q=Cartesian - other then if nops(q2)=3 then q3:=(parse(Join(["cartesian",convert(q2,string)],""))) else return;end if; else if nops(q2)=2 then q3:=(parse(Join([convert(q,string),convert(q2,string)],""))) else return;end if; end if; Do(%MathContainer32 = MathML[Export]([op(0,q3),[op(q3)]])); Do(%Label14(visible) = true): Do(%Label15(visible) = true): Do(%Label16(visible) = true): Do(%MathContainer33(visible) = true); Do(%MathContainer34(visible) = true); Do(%MathContainer35(visible) = true); Do(%Button35(visible) = true); Do(%Button37(visible) = true); Do(%Button38(visible) = true); Do(%Button36(visible) = true); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in Do(%MathContainer33 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in module() local q1,q2,q3; Do(q1 = %MathContainer33); Do(q2 = %MathContainer34); Do(q3 = %MathContainer35); if nops([q1])*nops([q2])*nops([q3])=0 then return;end if; Do(%Label17(visible) = true); Do(%Label18(visible) = true); Do(%Label19(visible) = true); Do(%Label20(visible) = true); Do(%Label21(visible) = true); Do(%MathContainer36(visible) = true); Do(%MathContainer37(visible) = true); Do(%MathContainer38(visible) = true); Do(%MathContainer39(visible) = true); Do(%Button39(visible) = true); Do(%Button40(visible) = true); Do(%Button41(visible) = true); Do(%RadioButton0(visible) = true); Do(%RadioButton1(visible) = true); Do(%RadioButton0(value) = true); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in Do(%MathContainer34 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in Do(%MathContainer35 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in Do(%MathContainer36 = NULL); Do(%MathContainer37 = NULL); Do(%MathContainer38 = NULL); end use;

use DocumentTools in Do(%MathContainer39 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=

use DocumentTools in Do(%MathContainer40 = NULL); Do(%MathContainer41 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in module() local q1,q2,q3,q4; Do(q1 = %MathContainer36); Do(q2 = %MathContainer37); Do(q3 = %MathContainer38); Do(q4 = %MathContainer39); if nops([q1])*nops([q2])*nops([q3])*nops([q4])=0 then return;end if; Do(%Button42(enabled) = true); Do(%MathContainer40(visible) = true); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools, VectorCalculus in module() local q, F1, F2, F3, F, a,b,c,rad, DIR; Do(F1 = %MathContainer33); Do(F2 = %MathContainer34); Do(F3 = %MathContainer35); if nops([F1])*nops([F2])*nops([F3])=0 then return;end if; F := VectorField([F1,F2,F3],coords=xxxVFconstruct:-q3); Do(a = %MathContainer36); Do(b = %MathContainer37); Do(c = %MathContainer38); Do(rad = %MathContainer39); if nops([a])*nops([b])*nops([c])*nops([rad])=0 then return;end if; Cent := Vector([a,b,c],coords=cartesian[x,y,z]); if Do(%RadioButton0) then DIR:=outward else DIR:=inward;end if; q := Flux(F,Sphere(Cent,rad,DIR),inert); Do(%MathContainer40 = q); Do(%Button43(enabled) = true); Do(%Button44(enabled) = true); Do(%MathContainer41(visible) = true); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer40); Do(%MathContainer40 = subsop([1,1] = simplify(op([1,1],q)),q)); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

use DocumentTools in module() local q; Do(q = %MathContainer40); Do(%MathContainer41 = value(q)); Do(%Button45(enabled) = true); Do(%Button46(enabled) = true); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer41); Do(%MathContainer41 = simplify(q)); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer41); Do(%MathContainer41 = evalf(q)); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

<Text-field style="Heading 1" layout="Heading 1">Solution (Maple 15)</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Data Entry</Text-field>

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Context Menu: Assign Name

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assign( );

Context Menu: Assign Name

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assign( );

Set the coordinate system

Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Vector Algebra and Settings\342\211\273Set Coordinates

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Set Coordinates

use DocumentTools in Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); Do(%ComboBox0(enabled) = true); Do(%ComboBox1(enabled) = false); Do(%ComboBox6(enabled) = false); Do(%Label0(enabled) = true); Do(%MathContainer0(visible) = true); SetProperty(Button0,enabled,true); Do(%MathContainer1(visible) = true); if Do(%ComboBox0) = Cartesian [x,y] then Do(%MathContainer0 = MathML[Export]([x,y]));end if; end use;

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use DocumentTools in Do(%ComboBox0(enabled) = false); Do(%ComboBox1(enabled) = true); Do(%ComboBox6(enabled) = false); Do(%Label0(enabled) = true); Do(%MathContainer0(visible) = true); SetProperty(Button0,enabled,true); Do(%MathContainer1(visible) = true); Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); end use;

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use DocumentTools in Do(%ComboBox0(enabled) = false); Do(%ComboBox1(enabled) = false); Do(%ComboBox6(enabled) = true); Do(%Label0(enabled) = true); Do(%MathContainer0(visible) = true); SetProperty(Button0,enabled,true); Do(%MathContainer1(visible) = true); Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); end use;

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Cartesian [x\134,y],Cartesian [x\134,y\134,z],Cartesian - other,polar,cylindrical,sphericaluse DocumentTools in module() local q; Do(q = %ComboBox0): if q=Cartesian [x,y] then Do(%MathContainer0=MathML[Export]([x,y])); elif q=Cartesian [x,y,z] then Do(%MathContainer0=MathML[Export]([x,y,z])); elif q=Cartesian - other then Do(%MathContainer0=NULL); elif q=polar then Do(%MathContainer0=NULL); elif q=cylindrical then Do(%MathContainer0=NULL); elif q=spherical then Do(%MathContainer0=NULL); end if: Do(%MathContainer1 = NULL); end module; end use;

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bipolar,cardioid,cassinian,elliptic,hyperbolic,invcassinian,logarithmic,logcosh,parabolic,rose,tangentuse DocumentTools in Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); end use;

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bipolarcylindrical,bispherical,cardioidal,cardioidcylindrical,casscylindrical,conical,ellcylindrical,hypercylindrical,invcasscylindrical,logcylindrical,logcoshcylindrical,oblatespheroidal,paraboloidal,paracylindrical,prolatespheroidal,rosecylindrical,sixsphere,tangentcylindrical,tangentsphere,toroidaluse DocumentTools in Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); end use;

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use DocumentTools, VectorCalculus in module() local q,q1,q2,q3; if Do(%RadioButton4) then Do(q = %ComboBox0); Do(q1 = %MathContainer0); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if q=Cartesian [x,y] then q3 := parse(StringTools:-Join(["cartesian",convert(q2,string)],"")); elif q=Cartesian [x,y,z] then q3 := parse(StringTools:-Join(["cartesian",convert(q2,string)],"")); elif q=Cartesian - other then if nops(q2)=2 or nops(q2)=3 then q3:=(parse(StringTools:-Join(["cartesian",convert(q2,string)],""))) else return;end if; elif q=polar then if nops(q2)=2 then q3:=(parse(StringTools:-Join(["polar",convert(q2,string)],""))) else return;end if; elif q=cylindrical then if nops(q2)=3 then q3:=(parse(StringTools:-Join(["cylindrical",convert(q2,string)],""))) else return;end if; elif q=spherical then if nops(q2)=3 then q3:=(parse(StringTools:-Join(["spherical",convert(q2,string)],""))) else return;end if; end if; Do(%MathContainer1 = MathML[Export]([op(0,q3),[op(q3)]])); SetCoordinates(q3); elif Do(%RadioButton5) then Do(q = %ComboBox1); Do(q1 = %MathContainer0); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if nops(q2)<>2 then return; end if; q3 := parse(StringTools:-Join([convert(q,string),convert(q2,string)],"")); Do(%MathContainer1 = MathML[Export]([op(0,q3),[op(q3)]])); SetCoordinates(q3); elif Do(%RadioButton6) then Do(q = %ComboBox6); Do(q1 = %MathContainer0); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if nops(q2)<>3 then return; end if; q3 := parse(StringTools:-Join([convert(q,string),convert(q2,string)],"")); Do(%MathContainer1 = MathML[Export]([op(0,q3),[op(q3)]])); SetCoordinates(q3); else return; end if; end module; end use;

use DocumentTools, VectorCalculus in Do(%RadioButton7 = true): Do(%MathContainer0 = NULL): Do(%MathContainer1 = NULL): Do(%ComboBox0 = "Cartesian [x,y]"): SetProperty(ComboBox0,enabled,false): Do(%ComboBox1 = bipolar): SetProperty(ComboBox1,enabled,false): Do(%ComboBox6 = bipolarcylindrical): SetProperty(ComboBox6,enabled,false): SetProperty(Label0,enabled,false): SetProperty(MathContainer0,visible,false): SetProperty(MathContainer1,visible,false): SetProperty(Button0,enabled,false): SetCoordinates(cartesian); end use;

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<Text-field style="Heading 2" layout="Heading 2">Volume Integral</Text-field>

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Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Integration\342\211\273Multiple Integration\342\211\2733-D\342\211\273Over a Sphere

Integrate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= over a Sphere

use DocumentTools in Do(%MathContainer44 = NULL); end use;

use DocumentTools in Do(%MathContainer45 = NULL); Do(%MathContainer46 = NULL); Do(%MathContainer47 = NULL); end use; Radius =

use DocumentTools in Do(%MathContainer48 = NULL); end use;

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use DocumentTools,VectorCalculus in module() local f, a,b,c, R, q; Do(f = %MathContainer44); Do(a = %MathContainer45); Do(b = %MathContainer46); Do(c = %MathContainer47); Do(R = %MathContainer48); if nops([f])*nops([a])*nops([b])*nops([c])*nops([R])=0 then return;end if; q := int(f,[x,y,z]=Sphere(<a,b,c>,R,[rho,phi,theta]),inert); Do(%MathContainer49 = q); end module; end use;

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use DocumentTools in module() local q; Do(q = %MathContainer50); if nops([q])=0 then return;end if; Do(%MathContainer50 = simplify(q)); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer50); Do(%MathContainer50 = evalf(q)); end module; end use;

use DocumentTools in Do(%MathContainer44 = NULL); Do(%MathContainer45 = NULL); Do(%MathContainer46 = NULL); Do(%MathContainer47 = NULL); Do(%MathContainer48 = NULL); Do(%MathContainer49 = NULL); Do(%MathContainer50 = NULL); end use;

<Text-field style="Heading 2" layout="Heading 2">Flux Integral</Text-field>

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Context Menu: Assign to a Name\342\211\273F

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Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Vector\342\211\273Integration\342\211\273Flux\342\211\2733-D\342\211\273Through a Sphere

Flux through a Sphere

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For the Vector Field:

use DocumentTools in Do(%ComboBox5(value) = "Select Coordinate System"): Do(%MathContainer51 = NULL); Do(%MathContainer52 = NULL); Do(%MathContainer53 = NULL); Do(%MathContainer54 = NULL); Do(%MathContainer55 = NULL); Do(%MathContainer60 = NULL); Do(%MathContainer61 = NULL); Do(%MathContainer56 = NULL); Do(%MathContainer57 = NULL); Do(%MathContainer58 = NULL); Do(%MathContainer59 = NULL); Do(%MathContainer51(visible) = false); Do(%MathContainer52(visible) = false); Do(%MathContainer53(visible) = false); Do(%MathContainer54(visible) = false); Do(%MathContainer55(visible) = false); Do(%MathContainer60(visible) = false); Do(%MathContainer61(visible) = false); Do(%MathContainer56(visible) = false); Do(%MathContainer57(visible) = false); Do(%MathContainer58(visible) = false); Do(%MathContainer59(visible) = false); Do(%Label24(visible) = false); Do(%Label25(visible) = false); Do(%Label26(visible) = false); Do(%Label27(visible) = false); Do(%Label28(visible) = false); Do(%Label29(visible) = false); Do(%Label30(visible) = false); Do(%Label31(visible) = false); Do(%Label32(visible) = false); Do(%Button57(visible) = false); Do(%Button58(visible) = false); Do(%Button60(visible) = false); Do(%Button61(visible) = false); Do(%Button59(visible) = false); Do(%Button65(enabled) = false); Do(%Button66(enabled) = false); Do(%Button67(enabled) = false); Do(%Button68(enabled) = false); Do(%Button69(enabled) = false); Do(%Button62(visible) = false); Do(%Button63(visible) = false); Do(%Button64(visible) = false); Do(%RadioButton2(visible) = false); Do(%RadioButton3(visible) = false); end use;

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Select Coordinate System,Cartesian [x\134,y\134,z],Cartesian - other,cylindrical,spherical,bipolarcylindrical,bispherical,cardioidal,cardioidcylindrical,casscylindrical,conical,ellcylindrical,hypercylindrical,invcasscylindrical,logcylindrical,logcoshcylindrical,oblatespheroidal,paraboloidal,paracylindrical,prolatespheroidal,rosecylindrical,sixsphere,tangentcylindrical,tangentsphere,toroidaluse DocumentTools in module() local q; if GetProperty(ComboBox5,value) = "Select Coordinate System" then Do(%Label24(Visible) = false); Do(%MathContainer51 =NULL); Do(%MathContainer51(visible) = false); Do(%Button57(visible) = false); Do(%MathContainer52 = NULL); Do(%MathContainer52(visible) = false); return;end if; Do(q = %ComboBox5); if q=Cartesian [x,y,z] then Do(%MathContainer51=MathML[Export]([x,y,z])); elif q=Cartesian - other then Do(%MathContainer51 = NULL); else Do(%MathContainer51 = NULL); end if: Do(%MathContainer52 = NULL); Do(%Label24(visible) = true); Do(%MathContainer51(visible) = true); Do(%Button57(visible) = true); Do(%MathContainer52(visible) = true); #Do(%MathContainer54 = NULL); #Do(%MathContainer55 = NULL); end module; end use;

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use DocumentTools, StringTools in xxxVFconstruct := module() local q,q1,q2; export q3; Do(q = %ComboBox5); Do(q1 = %MathContainer51); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if q=Cartesian [x,y,z] then q3 := parse(Join(["cartesian",convert(q2,string)],"")); elif q=Cartesian - other then if nops(q2)=3 then q3:=(parse(Join(["cartesian",convert(q2,string)],""))) else return;end if; else if nops(q2)=2 then q3:=(parse(Join([convert(q,string),convert(q2,string)],""))) else return;end if; end if; Do(%MathContainer52 = MathML[Export]([op(0,q3),[op(q3)]])); Do(%Label25(visible) = true): Do(%Label26(visible) = true): Do(%Label27(visible) = true): Do(%MathContainer53(visible) = true); Do(%MathContainer54(visible) = true); Do(%MathContainer55(visible) = true); Do(%Button58(visible) = true); Do(%Button60(visible) = true); Do(%Button61(visible) = true); Do(%Button59(visible) = true); end module; end use;

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use DocumentTools in Do(%MathContainer53 = NULL); end use;

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use DocumentTools in module() local q1,q2,q3; Do(q1 = %MathContainer53); Do(q2 = %MathContainer54); Do(q3 = %MathContainer55); if nops([q1])*nops([q2])*nops([q3])=0 then return;end if; Do(%Label28(visible) = true); Do(%Label29(visible) = true); Do(%Label30(visible) = true); Do(%Label31(visible) = true); Do(%Label32(visible) = true); Do(%MathContainer56(visible) = true); Do(%MathContainer57(visible) = true); Do(%MathContainer58(visible) = true); Do(%MathContainer59(visible) = true); Do(%Button62(visible) = true); Do(%Button63(visible) = true); Do(%Button64(visible) = true); Do(%RadioButton2(visible) = true); Do(%RadioButton3(visible) = true); Do(%RadioButton2(value) = true); end module; end use;

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use DocumentTools in Do(%MathContainer54 = NULL); end use;

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use DocumentTools in Do(%MathContainer55 = NULL); end use;

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use DocumentTools in Do(%MathContainer56 = NULL); Do(%MathContainer57 = NULL); Do(%MathContainer58 = NULL); end use;

use DocumentTools in Do(%MathContainer59 = NULL); end use;

use DocumentTools in Do(%MathContainer60 = NULL); Do(%MathContainer61 = NULL); end use;

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use DocumentTools in module() local q1,q2,q3,q4; Do(q1 = %MathContainer56); Do(q2 = %MathContainer57); Do(q3 = %MathContainer58); Do(q4 = %MathContainer59); if nops([q1])*nops([q2])*nops([q3])*nops([q4])=0 then return;end if; Do(%Button65(enabled) = true); Do(%MathContainer60(visible) = true); end module; end use;

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use DocumentTools, VectorCalculus in module() local q, F1, F2, F3, F, a,b,c,rad, DIR; Do(F1 = %MathContainer53); Do(F2 = %MathContainer54); Do(F3 = %MathContainer55); if nops([F1])*nops([F2])*nops([F3])=0 then return;end if; F := VectorField([F1,F2,F3],coords=xxxVFconstruct:-q3); Do(a = %MathContainer56); Do(b = %MathContainer57); Do(c = %MathContainer58); Do(rad = %MathContainer59); if nops([a])*nops([b])*nops([c])*nops([rad])=0 then return;end if; Cent := Vector([a,b,c],coords=cartesian[x,y,z]); if Do(%RadioButton2) then DIR:=outward else DIR:=inward;end if; q := Flux(F,Sphere(Cent,rad,DIR),inert); Do(%MathContainer60 = q); Do(%Button66(enabled) = true); Do(%Button67(enabled) = true); Do(%MathContainer61(visible) = true); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer60); Do(%MathContainer60 = subsop([1,1] = simplify(op([1,1],q)),q)); end module; end use;

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use DocumentTools in module() local q; Do(q = %MathContainer60); Do(%MathContainer61 = value(q)); Do(%Button68(enabled) = true); Do(%Button69(enabled) = true); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer61); Do(%MathContainer61 = simplify(q)); end module; end use;

use DocumentTools in module() local q; Do(q = %MathContainer61); Do(%MathContainer61 = evalf(q)); end module; end use;

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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