Question 10: I want to compute the definite integral . How can I tell Maple that is positive? In general, how can I declare a name to be positive, real, integral, even, odd, etc.

Answer: In Maple version V, you can declare a name to be a positive or negative as follows.

> signum(u) := 1; # Tell Maple that u > 0

                                 signum(u) := 1

> integrate( exp(-u*t) * ln(t)^2, t=0..infinity );

                        2                         2        2
                   ln(u)      ln(u) gamma       Pi    gamma
                   ------ + 2 ----------- + 1/6 --- + ------
                      u            u             u       u

Note, you must make the declaration BEFORE you try to compute the integral because Maple remembers the results of previous integrations. There is no ability to make any other kinds of declarations. Such a facility that supports more general types of declarations is presently being developed and will be available in the next release of Maple, Maple V release II.