A few sample Maple commands:

To find the definite integral of a function:
> integrate(sqrt(1-x^2),x=0..1);

To compute a double integral for the volume in the first octant under the plane 2x + 3y + z = 12:
> integrate(integrate(12-2*x-3*y,y=0..4-2/3*x),x=0..6);

To compute the triple integral for M_xy, the moment about the xy plane of the paraboloid between z = x² + y² and z = h:
> integrate(integrate(integrate(z*r,z=r^2..h),r=0..sqrt(h)),theta=0..2*Pi);

To graph a function:
> plot(sin(1/x),x=0..1);

To plot a function in polar coordinates:
> with(plots):
> polarplot(cos(3*t),t=0..2*Pi);