As someone who just signed up for an open university this semester, I'd love to hear opinions about Octave and Maxima for general purpose use. Especially for study, such as replacing Wolfram Alpha's step-by-step solutions.
I'm a Linux user and prefer an open-source solution. But I have no objection to paying a reasonable amount of money for a good commercial solution. Maybe Maple is worth looking at?
It depends on what your need is. I used Maxima (wxMaxima) for a quick prototyping of handwritten formulations and as a reference for some simplifications, roots etc.
Of course, its CAS capabilities are still useful. But I find that simplifications done on paper are often more straighforward, than making some expressions transform into the expected form in Maxima. Also, it's somewhat handy to have the ability to output the formulas in TeX format.
I vaguely remember Maple being more apt at expected simplifications.
Either way, I believe that Sage, Octave, Maxima etc. should be rather supplemental to textbook-based learning. In such way their results won't appear as pure magic, but as somewhat expected outcome of analysis.
I think it highly depends on what kind of math you're expecting (and how heavily you want to rely on a CAS). If most of your work is just simplifying equations and computing numerical solutions, basically any system will do whether that's Octave, Sympy + Numpy, etc.
I haven't used Maple for a while so can't speak to it's current functionality but there's been several times I've wanted to do something in Sympy/Octave and haven't found it whereas I can almost always get Mathematica to do what I want with a quick search. I tend to rely heavily on it for some more complicated/specific symbolic operations (e.g. symbolically transforming probability distributions) and for that use case, I haven't found anything better.
I'll also say that if your use case if more numerical/programming oriented, the language used might be an important factor. I personally don't like Wolfram Language and use very few of its language features and prefer Python for anything that Mathematica isn't suited for out of the box.
I prefer Python to Octave and Maxima. Numpy, scipy, and matplotlib for numerical stuff, and sympy for symbolic stuff. Having them together in the same general purpose language is really convenient, and Jupyter notebooks are fantastic. Sage is also good, but I've moved on to sympy. I don't know a way to get step-by-step working from a library, but sympy gamma can do some, so it's probably possible to some extent.
My experience suggests avoiding Maple like the plague. Sympy (and Sage) can do everything I ever used it for much nicer and easier.
I'm a Linux user and prefer an open-source solution. But I have no objection to paying a reasonable amount of money for a good commercial solution. Maybe Maple is worth looking at?