What is the definition of a problem
A problem is anything you're trying to solve computationally. Problems typically specify an input and a desired output which, for most models of computation, will both be finite. Any statement of the form, "Given $X$, compute/evaluate/find/determine/decide whether/..." is a problem.

So, yes, all the things you describe in the question are problems. (Though, in the case where the input is the uncountable set&nbsp;$\mathbb{R}$, you need to be careful about how you specify what the input is.)