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Other 196's:
What tools to to replace math work besides calculator?
Mathematica is one example that solves integrals and do some elementary proof run-down for you.
Granted that it is used mostly by STEM students. But I rarelly see someone totally forbiding the use of Mathematica as learning tool.
If you want a more High-school tool, then geogebra is another great example (and also opensource.
Pretty useful to plot the graphs and help you see what you're getting wrong.
I'm answering just to show that there are indeed mathematical tools used for the inbetween of a full math major and a "paltry peasant" that only needs to compute a good enough function for his problem be it an engineer working beams load, a chemist working enthalpy reactions or an biologist trying to find an EDO that best fits the data of prey/predator in a given ecosystem.