>>Medicare was billed 3935.00 by the hospital and received 234.00 in the agreed to price. Why would they bill 4000 to receive 234?

This is more complicated than you might think, including the Medicare schedule of fees and millions of medical necessity rules. If this is a hospital claim then it may or may not include hospital charges, e.g. depending whether you were in a lab or at home. Those get paid on a different Medicare "Part" that doesn't usually involve you.
How much the physician gets and how much you are charged, also depends on quite a few things including whether it's an assigned or unassigned claim. If assigned, it means the physician agreed to accept the scheduled fee as full payment. Yours sounds like an assigned claim, so the "agreed to" may represent the physician fee in isolation. Certainly $3935 sounds expensive for a physician fee unless they had to supervise the whole thing so I'm expecting the rest is hospital and other charges that will be covered under Part A. Sorry to appear vague, but Medical billing is an arcane art!