maxima

A full featured computer algebra system,
doing symbolic manipulation of polynomials, matrices, rational
functions, integration, Todd-coxeter, graphing, bigfloats. It has a
symbolic debugger source level debugger for maxima code. Maxima is
based on the original Macsyma developed at MIT in the 1970's.
It comes with extensive self tests.

What a snappy app cannot provide is allowing an external web browser
to open the offline manual it comes bundled with.