Here are some sample Maple assessment questions for this chapter.

1. Use Maple and the definition of the triple integral to evaluate the integral

   ó õ ó õ ó õ [ 0,1] ×[ 0,1] ×[0,1]     ( 4xy+3z2) dV

2. Create a worksheet which illustrates and utilizes the trapezoidal rule in both the x and y directions to estimate the volume of the solid under the graph of a non-negative function z = f(x,y) over a type I region.
3. Implement the following in Maple: Here is a way to estimate a double integral of the form

   ó õ 1 0  ó õ 1 0  f( x,y) dydz

   where 0 £ f( x,y) £ 1 for all ( x,y) in the unit square. Choose x,y,z uniformly randomly between 0 and 1, and then evaluate f( x,y) . Count all those points ( x,y,z) for which z £ f( x,y) and ignore the others. The total count divided by 1,000 will thus be an estimate of the value of the double integral.
4. Create a worksheet which estimates and illustrates the center of mass of a given solid assuming uniform density. The worksheet should plot both the solid as a wireframe (or using transparency) and its center of mass.
5. Create a worksheet which first allows a user to supply 4 points and then computes the volume of the tetrahedron whose vertices are the 4 given points.