Take a look at the sentence again:
As her teachers had recommended, Madison
tried to study in the library but discovered that the good music, unlimited
soda, and big tables at the campus café made a great place to do homework
during fall semester, Madison must have eaten 150 pizza slices while she
slogged through Fundamentals of Biology.
The comma between recommended and Madison is completely correct. As her teachers had recommended is a subordinate clause, so it cannot stand alone. Madison tried to study in the library ... begins a main clause. When a subordinate clause introduces a main clause, you need a comma between them.
Go back to the sentence to try again.