>>It's after school and you are stuck doing the clean up work with Mayumi. You are all alone with her in the classroom, what do you do?
99% of /a/. Just clean up the room and never speak. Try to take glances at her whenever you think she isn't looking. Have an awkward quick 'see you tomorrow' after everything is done and run out of the classroom towards home.
Myself, I’d just do what I normally do in the presence of anyone. Ask what she would want to do as her part of the cleaning duty. In that question, I’d insert a suggestion that she’d pick me to do one or another of the less fun duties and make a joke of it to lighten the mood and to start up a possible conversation. If you can’t see where it goes on from there, you are obviously one of those lonely people who don’t know how to talk to the opposite sex.