Translation:What should I do?
"怎么办“ is a set phrase. It sort of means "what should I/we do?" A more literal translation would be more like "how should I proceed now?" This is asking how to navigate a situation or solve a problem. This phrase isn't used to ask something like "what should I do on my day off?" For that, you could use “做什么？”
Apparently, zenme ban is a phrase that means what to do. So it's just a phrase that doesn't mean what it literally would mean, like in English you have for example "what's up" but you're not asking about anything that is up.
So its an idiom. Does that mean the more literal way mentioned above works too?
办 also means 'to manage' or 'to handle', so maybe you can think of it as 'How can I deal with this situation', 'How can I cope with this?' or 'How should I handle this?'
On another app (Memrise) I am using 怎么办 is translated as "what to do". Perhaps 做 is used with a specific activity whereas 怎么办 is used without one? This is speculation. I have a Living Languages Mandarin program and one of the speakers asks another 你在做什么?
In my opinion the idea of "how" (怎么办) here refers to "in what way should I do", not "to what extent should I do" as you might have mistook.
If you look in pleco for 办 one of its examples is almost the same as this: 我该怎办 for "what shall i do".