Ouch, that's a good point. Well, I don't think there's any way to solve that problem with the data that's provided. The operator hash would need to specify which operators are commutative and which aren't.
In fact, the problem requirements state:
Operations of the same priority can be considered to be commutative, and can be evaluated in any order.
So, I solved the problem as stated, although the problem as stated doesn't quite reflect actual arithmetic.
Update: Oops, I'm confusing commutative (order doesn't matter) with associative (grouping doesn't matter). Subtraction is neither commutative nor associative, but the problem MeowChow pointed out involves associativity. The operator hash would need to specify which operators are associative. Either way, there's not enough information available for a perfect solution.