pocket underpair vs overcards 10 10 hand vs qxx flop

[Downstream 0]

This is .25/.50 Limit Hold Em. I am middle position, have 10 10, raise and there are 5 callers. Flop is qxx. It is checked to me.Assume this is a rainbow flop, but if you would play differently with a two flush out, take that into account (see below).Does anyone have an opinion on this? This situation comes up repeatedly, your raised pocket pair against one overcard. I don't like to let this go checked around the table and have no information on the hands of the other players.Semi-BluffUsually I will bet out on this, to test the waters. I will do this if there is one overcard like a J or maybe Q over my 10s. A two overcard flop means check-fold. If its raised, I fold. If called, then they probably have nothing and I will often get a free card on the turn. The theory here is that I know where I am this way and can save the larger bet on the turn.Check-RaiseThe other theory is to not bet, but check raise instead. I don't usually do this, but maybe someone can comment on it. This costs 2 bets however so has to work better. When I check raise, the calling stations will usually fold to an unfamiliar play like a check raise. A few will call and the original bettor will reluctantly call. If the bettor raises, I fold. This play backfires if it is checked around.Check-Fold with two flush on flop?If there is a two flush on the flop, I don't know if its better to check-fold, become a calling station, or try one of the above strategies. Thanks for your help.