I can't seem to get a straight answer for this question, but how can calculus be applied in real-world contexts where a function isn't already known?

For example, say you want to find the volume of a hill. This can be done with practically any precision you like, so long as you have a curve function to integrate. You take the integral from x = 0 at the beginning to the final x value in meters, etc. You can use Riemann sums to get a close approximation and integrate twice (the second with the curve function looking at the hill rotated 90 degrees).

This is fine with a curve function, but how is it possible to even create a function x that appropriately fits the height of the hill at each value x? I mean, you can make a domain/range table, but solving for y at each point can yield a different function altogether (if the tangent at a point x is drastically different from the preceding and succeeding points the function must be redefined and becomes a composite).

I fully understand integration and derivation when the numbers are given, but how does this apply to real-world things that aren't manufactured with specific values?