Google given the following definitions of 'expect':
regard (something) as likely to happen.
"we expect the best"
"a 10 percent rise was expected"
regard (someone) as likely to do or be something.
"they were not expecting him to continue"
"I expect she'll be late"
believe that (someone or something) will arrive soon.
"Celia was expecting a visitor"
look for (something) from someone as rightfully due or requisite in the circumstances.
"we expect great things of you"
"we expect total loyalty"
I'd wager that the dictionary that the student consulted was presenting a simplified form of one of these meanings, possibly the first. One of the synonyms Google lists is "anticipate", which can indicate some emotional component of wanting the result to happen; this is probably where "look forward to" came from.
The meaning of the student's sentence isn't "I'm excited about getting to draw a cartoon;" it's "I think I will be drawing a cartoon."
I would have phrased it a bit differently:
I'm taking an art class on modern media this semester. I'm expected to draw a cartoon.
And I would also propose that the dictionary that the student consulted is wrong. Such things do happen. It could also be that the dictionary had listed "anticipate" as a definition, and the student had then looked up "anticipate" and found the definition "to look forward to". That's actually a listed definition of "anticipate", but not in any listing of "expect" I've found so far.
To see Google's definition for a word, go to Google and search "define [word]". So the definition of "expect" cam be found by searching "define expect".