Translation:The hospital shall pay for my treatment.
Would "should" be accepted in place of "shall"? I put "shall" based on the hints, but I would never say "shall" in real life or writing. It ("shall") strikes me as very old-fashioned word that is going out of use, except in legalese. On the other hand, "should" and "shall" don't always mean the same thing. In general, I would use "will" if I meant I was going to do something in the future, and "should" if I ought to do something. "shall" can be used in either situation (although the latter I've only seen in things like the ten commandments e.g., "Thou shall...").
Fun fact: even lawyers are encouraged by the US government to never use the word "shall" in any context.