Few people know and use the GNU Emacs-Calculator for beyond routine arithmetic. Calc is an extremely flexible and powerful mathematical tool, capable of everything from symbolic differentiation to matrix algebra to modulo arithmetic.
This is a Screencast showing a tiny few of its advanced features that I've been using for a couple of years now. This also doubles as a gentle (but incomplete) introduction to Calc for Emacs users. (It goes a bit slow so you can follow along in Emacs.)