Computing triple integrals with Maple proceeds in a similar fashion. For example, the command to perform the following integral
is
> int(int(int(exp(x)*y*z^2,x=0..1),y=1..2),z=-1..1);
It is sometimes helpful when you aren't sure you have the command right to use the Int command, which is an inert form of the int command. Inert means that Maple just displays the integral and does not try to evaluate it. Here is an example.
> Int(Int(Int(exp(x)*y*z^2,x=0..1),y=1..2),z=-1..1);
By using the inert Int command, you can easily check that the limits and the order of integration are correct.
More complicated triple integrals can also be done. For example, the
volume of the region bounded by the paraboloid 
and the
plane z=y+2 is given by the triple integral
This integral can be computed with the following Maple command.
> int(int(int(1,x=-sqrt(z-y^2)..sqrt(z-y^2)),z=y^2..y+2),y=-1..2);
