The Maple `int` command will handle most integrals that can be
done analytically. Both definite and indefinite integrals can be done,
as shown by the following examples.

> int(x^2,x);

> int(x^2,x=0..2);

> int(sin(4*x),x);

> int(x*(3*x^2+2)^(5/3),x);

Notice that Maple doesn't include a constant of integration for indefinite integrals.

Unfortunately, there are lots of integrals that can't be done
analytically. (The ones that can be done tend to appear in calculus
texts. The ones that can't be done often appear in real life.) When
Maple can't do an integral, it simply returns it unevaluated. The
example below show how to use the `evalf` command to get Maple to
evaluate the integral numerically.

> int(cos(x^3),x=0..1);

> evalf(int(cos(x^3),x=0..1));

Maple uses a sophisticated numerical integration routine with automatic error control to evaluate definite integrals that it can't do analytically.

Thu Mar 27 08:41:19 EST 1997