Older editions of Thomas' Calculus had a really neat appendix called "Lies that your Computer and Calculator Told You", and it had a bunch of examples showing how to break, confuse or at least horribly slow down a lot of computational methods for some mathematical problems.

The point? Computers can never 'replace' math. They make things easier, but aren't a do-all end-all solution.

For example, try to use a TI-85 to find the derivative of the absolute value of x at x=0. The calculator tells you the answer is 0, when really it is undefined.

Sadly, that appendix seems to have disappeared from the newest edition (I could be wrong there).