I'm a bit of confused with と in the following sentence, what does it mean here and how can we translate the whole sentence?
Thank you very much for help!
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This text, even with the context taken into account, does not make much sense. 存分に refers to doing something seriously with one's full might. So it doesn't fit where the homework solves itself without human interventions.
I'd say this is a mistake of "その名に恥じず放置すればするだけ自然と進行してくれればそれは非常に楽だけど"
The previous line from the girl asks the boy to stop studying and play with her, so this line translates to something like "It'd be very convenient if it [the homework or something?] would make progress on its own just by literally leaving it alone [but it doesn't, so I have to do my homework]"