I'm not sure WHY you want to do this, so it is difficult to think of alternatives but assuming you are trying to print a report that you can get after selecting multiple parameters from the drop downs, then one of these ideas might help:
1) If you only need one set of values, set the drop downs manually to those values and look at the final url that is called. It's probably something like run_report.aspx?acedemic_year=2012&semester=fall. You could then use curl to call that directly.
2) Or: If you need to change the parameters, then find out where jquery is getting the values from, and get them yourself and then do (1)
Hope that helps