You have proved the 9 volt adapter is not broken. It will power things that need nine volts and it will be very close to the right voltage if they use 350ma of current. If you connect to a hundred dollar electric piano, it will probably work. If you connect to a $4 transistor radio that uses 10ma, you might smoke the capacitors inside it.
Even after you prove the adapter is not broken, you still have to consider if the machine you want to power will use most of the current, and if the machine is good quality or very cheap and has no ability to survive a few extra volts.
ps, your math is getting better.