What do you think caused you to dream up the existence of a backpack in this scenario ? Could it possibly be your subconscious desire to see the situation differently than presented not because the situation was grossly misrepresented but because the potential existence of gender biases makes you uncomfortable ? I can't say because I don't know you but eh, mull it over a bit.
The binder was sitting on my lab table right in front of me. I could have easily cheated that whole time really. The teacher who won't let somebody reach into a binder while looking away to get a calculator for fear of them cheating would not then suggest another student use a phone in a test if they were also worried about that person cheating. Which he should have been since I gave him no extra reason to suspect I would have cheated when I met him before the test and my regular teacher liked me. He knew nothing about either of us and therefore should have treated us both as potential cheaters or trustworthy students. Now, is it possible he could just have really bad problem solving skills ? Of course, which is why I never made a fuss about it but I'm not going to ignore the fact that all he really knew about either of us was our gender while reacting to us both very differently.
People think they are clever and they think they can understand other people easily by subconsciously picking up clues. I think that's largely because we make a ton of judgments about people but very few of them are ever vocalized or therefore challenged. So we naturally think most must be correct just because they haven't been disected and proven wrong.
In your own words you would actually refrain from cheating because you get something out of it. You learn. However, I really didn't need tests and assignments to learn stuff in order to get a good enough mark to be a good student. They were just annoying things I had to get done. My learning came partly from hearing teachers speak and mostly from watching YouTube videos. In college I liked reading over the material on my own for a lot of my courses and researching it myself in order to understand. The way other people learn isn't the way I learn. I had a friend actually who struggled a lot with science but when it came to the physics unit while everybody else was struggling she had no problem what so ever. The thing is though, the school system doesn't recognize that people can learn or be smart in different ways. It's just one system and if it doesn't work for you well sucks for you. So I didn't care about cheating partly because I might as well if they think I am anyways but also because not cheating didn't help me learn.
Then I suppose there's the idea that I would feel good about working hard and getting a good mark but that's a whole other can of worms for another day.