Maple can also be used to take some of the tedium out of calculations
of centroids and centers of mass. Suppose that a mass with density
function 
occupies the unit cube. Then the
following example shows how to compute the mass and the coordinates of
the center of mass of the body.
> mass := int(int(int(1-z/2,x=0..1),y=0..1),z=0..1);
> x_bar := int(int(int(x*(1-z/2),x=0..1),y=0..1),z=0..1)/mass;
> y_bar := int(int(int(y*(1-z/2),x=0..1),y=0..1),z=0..1)/mass;
> z_bar := int(int(int(z*(1-z/2),x=0..1),y=0..1),z=0..1)/mass;
