SYMBOLIC CALCULATORS

Recently I downloaded a free symbolic calculator called MuPad. It is indeed a wonderous piece of software. It does many of the same sorts of things that Mathematica and Maple do. For example, the command:

expand(cos(x + 2*y));

produces the result:

cos(x)cos2(y) - 2cos(y)sin(x)sin(y) - cos2(x)sin(y)

... and if I type in:

rewrite (sin(x)/cos(x),exp);

it responds with:

This is very impressive. But I have a question.

Outside of academia, who would weant to do this, 
and for what purpose?

Can someone give me a specific example, or is it sufficient to say that it's and academic exercise, and leave it that? I need an answer.

Go to http://www.calc101.com/webMathematica/MSP/Calc101/WalkD

Here you can have any expression differentiated or integrated. For example:
But again - will someone please write and describe to me situation in which someone would actually want to do this.