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You don't need a CAS for calculus. A scientific calculator will do fine, however, if you want to learn a CAS in general, I'd pick Maple.
Maple releases all their algorithms to the general public, but Mathematica does not.
If the symbolic functions aren't essential, I'll suggest a few open-source altenatives: octave and scilab. Both, octave and scilab, use Matlab-like syntax. Octave and scilab are more for doing numerical tasks, rather than evaluating an integral symbolically.
octave and scilab are great for doing linear algebra tasks: eigenvalues, matrice operations, and such. I've solved a few ODE's and PDE's numerically on them for fun. octave is a rather modular application. It supports writing programs or "external" functions in Java, C, and C++, in addition to its on C-like language. Octave is totally GPL'd, whereas scilab is nondistributable but open-source (?).
scilab and octave support graphing, also. Octave interfaces with an application called "gnuplot", which supports all the methods of graphing that the propiertary CAS's (Mathematica, Maple, etc.) support. I'm not as familiar with scilab but it uses something *very* similiar to gnuplot. I actually like the plotting features of scilab slightly better than those of gnuplot. Scilab supports real-time rotations and zooming, whereas gnuplot does not. Mathematica doesn't either.
Learning how to use the computer for numerical calculations is all what the computer is about; I find the CAS to be pointless.
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