My neighbor is growing this vegetable and forgot what kind of gourd it is. Is it a bottle gourd or a type of butternut squash?
And here's the flower:
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I'm fairly sure that's a bottle gourd. In my experience butternut squash fruits start out quite ovate and then develop a swelling when they get larger (or don't). Also all the butternut flowers I've seen have been yellow and much more trumpet shaped, and a quick google of bottle gourd flowers shows them to look very much like your photograph.