I use Mathematica as my advanced calculator. It’s a functional language with an extremely vast and consistent mathematical and non-mathematical library, top notch symbolic capabilities (SymPy is just child’s play in comparison), top notch numerical capabilities, and very decent performance. You certainly don’t need to write your own rotation function — well, 2D rotation is trivial, but what if you want 3D rotation around a vector? Mathematica’s got you covered. Got a command line mode too, see MathKernel.

The downside: it’s not free (as in beer or speech).