Algorithmically generated variables are used to generate random numbers in questions and create multiple permutations of questions from a single template.

You can use either Maple T.A. or Maple to generate algorithmic variables. You can use either (or both) types of variables in *any* question type.

The syntax for a Maple-based variable definition is:

<variable_i>=maple("<Maple_command>");

To define an algorithmic variable in the plain-text script file, specify variable definitions (or other variable control sequences) in the **algorithm** field.

algorithm=

<variable_definition_1>

...

<variable_definition_n>

@

In the **Question Editor**, define variables by directly entering Maple-based variable definitions on the algorithm screen or using the Algorithm Designer.

The following tutorial shows how to convert a static **Maple Formula** question to an algorithmically generated question by using variables assigned values by Maple commands.

Consider the following plain-text script question definition, which asks a student to enter an anti-derivative of **x^3**.

**qu.1.1.question=Enter an anti-derivative of x^3.@
qu.1.1.maple=evalb(diff($RESPONSE,x)=x^3)@
qu.1.1.type=formula@
qu.1.1.mode=Maple@
qu.1.1.allow2d=1@
qu.1.1.name=Maple AntiDerivative@
qu.1.1.comment=Any function of the form x^4/4 + C, where C is a constant, is an anti-derivative of x^3.@
qu.1.1.editing=useHTML@**

**Notes:**

- This question uses Maple to verify that the derivative of the student response is equal to
**x^3**. This is recommended in place of comparing the student response, which can have an additive constant, with the integral of**x^3**, that is evalb($RESPONSE=int(x^3,x)).

- If the student enters an incorrect response, the system display the value in the
**comment**field. In Maple-graded questions, if there is no**comment**field, the system returns the message**Comment: No feedback is provided with this question**.

To change this question to an algorithmic question, use the following plain-text script question definition.

**qu.1.2.question=Enter an anti-derivative of x^$exponent + ${coeff}x.@
qu.1.2.maple=evalb(diff($RESPONSE,x)=x^$exponent+$coeff*x)@
qu.1.2.type=formula@
qu.1.2.mode=Maple@
qu.1.1.allow2d=1@
qu.1.2.name=Maple AntiDerivative@
qu.1.2.comment=Any function of the form $answer + C, where C is a constant, is an anti-derivative of x^$exponent + ${coeff}x.@
qu.1.2.editing=useHTML@
qu.1.2.algorithm=$exponent=maple("randomize():rand(2..5)()");
$coeff=maple("randomize():rand(2..9)()");
$answer=maple("int(x^$exponent+$coeff*x,x)");
@**

**Notes:**

- You must follow the variable naming conventions.

- For a list of the guidelines for Maple commands in Maple-based variables, see
*The Algorithm Designer*.

- The variable
**$exponent**is assigned a value calculated by Maple using the**rand**function.**rand()**returns a random**12**-digit positive integer**rand(a)()**returns a random integer in the range**0 ... a-1**(inclusive)**rand(a..b)()**returns a random integer in the range**a ... b**(inclusive) For information on other Maple commands, see your Maple documentation.

- The Maple command:
**randomize():**is included so that a different value is generated for each question instantiation. You must include the**randomize():**command in every Maple-based variable definition. That is, it is required in the definition of**$exponent**and**$coeff**.

- The Maple command:
**int(x^$exponent,x)**calculates the correct answer, which is displayed using the**comment**statement if the student response is incorrect.

- The examples in
**Tutorial 1**can be converted to**Maple Syntax**questions by changing the type field value from**formula**to**maple**, and changing allow2d to 0 for text-entry mode. For**Maple Syntax**questions, it is recommended that you attempt to prevent a student from calculating the correct answer using Maple commands. For more information, see*Using Maple Code to Prevent Cheating in Maple Syntax Questions*.

For an example plain-text script that defines a Maple question with Maple plotting of the student response, see *Plotting a Student Response*.

You can also use Maple-based algorithmic variables in other question types.

The following plain-text script defines a **Formula** question that uses Maple-based variables.

**qu.1.3.question=What is the sum of $a and $b?@
qu.1.3.mode=Formula@
qu.1.3.name=Maple-based Variables in Formula@
qu.1.3.answer=$answer@
qu.1.3.editing=useHTML@
qu.1.3.algorithm=$a=maple("randomize():rand(100..200)()");
$b=rint(10,50);
$answer=int($a+$b);
@**

**Notes:**

- This question uses both Maple-based (for
**$a**) and Maple T.A. random variables (for**$b**).

- When referencing negative, random variables in a
**maple**variable definition, be sure to place the negative variable in parentheses, otherwise an error message will return.**$c=maple("$a + ($b)");**

**See Also:**