having a teenage sexual affair while pretending to be studying for Calculus, and hiding it from one's parents, also known as being tutored in any mathe realted subject.
"I'm off to study Cockulus with Ben. I'll be back in....tenminutes."
It means: a mutant combination between cockroach and mouse.
Robin: So what was it, a cockroach or a mouse?
Lily: It was a cockamouse!
Robin: What?
Lily: It's some sort of mutant combination of the two.
It's as if a cockroach and a mouse, you know...