So yesterday I learned about functionals, which my book claims are "machines that take a function and return a number", in contrast to functions, which take a number and return another number. I immediately thought of definite integration: it's an operation that takes a function, and returns a number. I did a Google search for this and found the Wikipedia page on functional integration, which says that a functional integral is an integral where the domain is not a region of space but a space of functions. Again, could the definite integral be a special case of this where the "space of functions" is just all of the values between the bounds of integration treated as constant functions? And finally, when you take the derivative of a function like 3x, which is of course 3, is that also a functional? This seems like a bit more of a stretch, because taking the derivative of a more complicated function like x^2 gives back 2x which is a function, not a number. Just wondering.