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This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on. ↗
If you just have a single problem to solve, then fine, go ahead and use a neural network. But if you want to do science and understand how to choose architectures, or how to go to a new problem, you have to understand what different architectures can and cannot do. ↗
You could write a song about some kind of emotional problem you are having, but it would not be a good song, in my eyes, until it went through a period of sensitivity to a moment of clarity. Without that moment of clarity to contribute to the song, it's just complaining. ↗