Recently (re-)discovered Mathematica, and found spanning a much larger set of domains than I expected (also, very approachable).
From the open source alternatives the better supported I think is (wx)Maxima, which for the simple tasks I usually require (i.e some Taylor series, check cumbersome trigometric equations, ...) it's more than enough although it's true it lacks by a long margin the polish of Mathematica. Recently I'm considering buying an educational version of Mathematica just for the convenience. It sucks it's a closed source program but it's rare, although not impossible, for open source alternatives to have the same good documentation and ease of use. I guess that the attention to these details is not something people usually do unless being paid.
Now, tangentially related, this is extremely cool (and previously posted in HN I think): https://ai.facebook.com/blog/using-neural-networks-to-solve-...