I only have experience with Mathematica. I use it a fair amount and love it, but it has a pretty steep learning curve to it (and you're most proficient if you think about it as a functional language, I've found). It makes doing complicated things quite easy and also has a LOT of syntactic sugar for messy things. What I really like about it is that you can do just about anything with it---write a function that works on images?
You can copy and paste an image directly from the internet as the argument to the function and it works fine. Realize you're actually doing calculus?
Throw that same image into an integral and Mathematica will spit out an answer. What that answer means, of course, is up to the programmer to figure out.
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