One of the principles of General Relativity is that test objects follow a geodesic unless otherwise acted upon by a force. From this perspective, it is clear that physicists, consciously or unconsciously, view the Pauli Exclusion Principle (PEP) as a force, since it is intrinsically involved in the processes that prevent us, for example, from following a geodesic through the earth's surface. If this interpretation is considered incorrect, so be it.
There are other instances where physicists treat PEP as a force. Semantic arguments aside, PEP is in fact a repulsive phenomenon that that keeps fermions from occupying the same state. It behaves like a de facto force, and can be overcome by sufficient pressure. What is the mathematical form, in terms of $r$, of PEP repulsion? Have experiments been done to determine this?
Regarding the fall-off with $r$: note that one electron approaching another electron must "know" at some distance that it is being repulsed; the two electrons need not come in contact.
[Author's note: Since several readers claim this is a duplicate question, official forum guidelines require I explain why it is not. First, I see nowhere else the question as to the mathemetical form of the EFFECTIVE repulsive force f(r). Thus, the question is new on this forum. Second, whether PEP repulsion is a "true" force, a "fundamental" force, or a "pseudo" force is a matter of semantics, discussions of which do not answer the question. In any case, PEP repulsion is an EFFECTIVE force, and therefore in principle can be described by some function f(r), even if only statistically.]