Trouper/trooper

Can anyone clear up a little arguement I'm currently involved in?

The phrase involved is "....like a trooper" OR
"....like a trouper"

Eg, swears like...., plays like...

I'm pretty convinced that it's the latter which is correct, as in trouper on the stage, gritty, show must go on etc etc. Anyone shed any light?

Cheers..

From the Associated Press Stylebook:

troop, troops, troupe -- A TROOP is a group of people or animals. TROOPS means several such groups, particularly groups of soldiers. Use TROUPE only for ensembles of actors, dancers, singers, etc.

I am going to guess that it's "swear like a trooper" (as in soldier) and "a real trouper" (as in an acting company, the show must go on. Now I am off to check Merriam-Webster.