It would be D. As long as your going to the store. This is because it describes under what circumstances you are to buy the bananas. Buy is the verb and the adverb phrase describes it.
The adverb clause in the sentence "As long as you're going to the store, would you buy some bananas?" is "as long as you're going to the store," which provides a condition for the request made in the main clause. Thus, the correct choice is D. This clause effectively modifies the main action of the sentence by indicating under what condition the action will take place.
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