A symbolic computation package allows one to conduct mathematical experiments. A symbolic computation package allows one to collect data about a problem being studied. This is similar to the way other scientists work. It is easier to try several different approaches to a problem and see which works. The machine is stupid.
Intelligence comes from the user.
The user thinks, the user interprets, the computer calculates. Syllabus Rational and real arithmetic in symbolic computation. Symbolic differentiation and integration. Writing Maple programs, procedures in Maple. The linear algebra package in Maple.