how many times will ModuleB be compiled?

Once ... unless you delete it's key/value pair from %INC, which Perl uses to determine if it's already loaded a particular module/file.

For details, see the "semantics similar to" code example in perldoc require, which I've excerpted the appropriate bits of (plus pointer comments) below for convenience.

sub require {
    my($filename) = @_;
    return 1 if $INC{$filename};     # <-- already loaded?
      # ... pull in the module
    $INC{$filename} = $realfilename; # <-- stop future reloads
    return $result;
}
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    --k.