The php manual (under the mysql api) saysd you can use mysql_create_db but you should issue an SQL command create database.
I would question why you want to do this, your explination about phpbb. If you want to create a completly new and seperate insall of phpbb you will need a new database, if you just want a new forum you can create that in an existing install.
If you had a seperate db for each forum you would have loads and loads and loads...
good luck
Kevin