A word which, like whom, has come to be thought of as overly formal and stuffy in American speech. In current use, it indicates a very strong intention or will to do something.
Traditionally, shall is used as an auxilliary to form the future tense for the first person: ("I" and "we")
I shall go
you will go
he/she/it will go
we shall go
they will go
the act of getting delayed in the bathroom stall because the guy in the next stall finished shitting at the same time as you, and you'd like to avoid the awkward encounter at the sink
"Should we now proceed? If you are in a situation where a group is gathering to do something (go out for lunch, start a meeting, etc.), "Shall we?" would mean something like "Are we now all ready and is it now time to proceed with what we are here for?". (Or more simply, "Should we now proceed?", but that explains "shall" in terms of "should".)
ok guys we got a go (and you tell to you friend) shall we? (ready to go?)