What function do "shall" and "must" serve?

I've been taught that the word "shall" represent obligatory or mandatory. On the other hand, I was taught by another lecturer that "must" represent mandatory.

Which one of the two represents obligatory? When I asked a teacher this question, he told me "shall" is also synonymous to might or maybe. Is this true?

As an example, consider:

• He shall report the case to his senior officer.
• He must report the case to his senior officer.

"Shall" is not synonymous with "might" or "maybe." It is synonymous with "will."

"Must" carries the semantics of mandatory action more than "shall."

In Australian and UK varieties of English (I can't speak for American) "shall" is on the way out, being replaced by "will." I think originally the semantic difference between the two words was that "shall" simply indicated that the action would take place in the future, and "will" had more of a personal intention element, but that distinction has disappeared.