Solution in the VectorCalculus Package
Use of the VectorCalculus package has three advantages. First, you can control the appearance of vectors with the BasisFormat command. The default setting causes vectors to be displayed as linear combinations of basis vectors. The setting chosen here causes vectors to be displayed as column vectors. To make the change, change "true" to "false" in the BasisFormat command.
Second, the Norm command defaults to the Euclidean norm and all quantities are treated as real. At top level, the vectors would also appear as columns, but the available vector norm would treat quantities as complex, and complex conjugates and absolute values would then appear.
Third, the int command is modified. At top level, int represents integration in a single variable, and does not automatically map to the components of a vector. In VectorCalculus, int can be used to represent iterated (multiple) integrals, and also maps automatically to vectors.
Because Maple understands the prime as a differentiation operator, it's a lot of work to override the prime and use it strictly as notation. Hence, R will be used for , and for . With these conventions, make the following definitions.
> 
`(x, 0, z)); 1" align="center" border="0">

The integrand will then be
> 

The electric field vector is then
> 

Notice that Maple has evaluated the integral and returned the electric field as a vector.
Setting and calling by the name gives the cylindrically symmetric solution obtained in Table 1.
> 

The reader should pay particular attention to a notational issue not obvious without comment. The name has been assigned a vector as its value. Ordinarily, this would persist in the substitution made into E. To avoid this clash, we have converted to an "atomic identifier" via Context Menu: 2D Math≻Convert To≻Atomic Identifier. The symbol is now seen by Maple as a name distinct from r.
Graphics
Figure 1 provides a graph of the electric field as a collection of arrows.

Figure 1 The electric field in

Figure 2 shows the electric field restricted to the plane.

Figure 2 The electric field drawn in the plane

To obtain field lines, solve the differential equations . The dependent variables in EE must explicitly be functions of the independent variable . Thus, write
> 

then obtain numeric solutions and a graph with the DEplot command, as shown in Figure 3.

Figure 3 Field plot of the electric field, along with several field lines.

Solution in the Physics Package
An alternative solution in the Physics package displays the unit basis vectors as , and vectors that are linear combinations of these vectors as symbols with an arrow superimposed.
> 

> 

Define the position vector as and the vector as by typing
> 
r_ := x*_i + z*_k;
R_ := Z*_k; 
and converting this text input to 2D Math Input via the Format≻Convert To menu options. The result will be
so that the integrand is
> 

The electric field vector is then
> 

The components of the electric field vector can be extracted as
> 

and
> 
