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But you are on the right track, if hero is behind a set here he does have 11 outs to beat it, 9 spades and the other 2 Queens. As mentioned above, if we are suspecting a set we'd rather not see a pair on the board ;-)
Mat


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But the queens would have to come runner-runner to make a full, otherwise your two pair are no good. Seeing as how there are 3 queens left, I don't think we can count them as even 1 full out, let alone 2.

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Except that if he does catch a queen on the turn then the aces become outs too.