Okay, let's get one thing out of the way. Getting a math PhD has rarely proven to be a useful choice in my life, so I wanted to try it here. But the integral is wrong! The two curves intersect at whole numbers (-1 and 3). Integrating 7-2x gives 7x-2x^2, so plugging in the bounds gives whole numbers. Integratings (x-2)^2 gives 1/3(x-2)^3, and neither bound gives a multiple of 3 when plugged in, so the answer should have 3 in the denominator. I thought there were supposed to be some impossible questions, like Baldi's Basics, but all the others were possible.
Anyway, this game made me think of 5 other pieces of media as I played: Deltarune, for the character creation screen; Ezekiel 16, for being a baby cast out into the wide world; an evil version of Phantom Tollbooth, with all of its unusual and allegorical characters; No End House, the creepypasta, for its succession of rooms that take an increasing toll on our protagonist; and Duke Bluebeard's Castle, my favorite opera and one where Bluebeard unlocks seven doors to show his wife that become increasingly disturbing.
In this game, you have to obtain seven keys from various challenges in order to restore a lighthouse. This world is weird; at one point you're a baby that walks around and grows bigger in seconds, and at another you have a mom you grew up with who raised you. So a lot of things are allegorical.
Each key that you get requires something different. One has a quiz; another requires you to get closer to someone. Many involve self-reflection of some kind. The pattern breaks down a bit at the end when things get more hectic.
Overall, I loved the visuals and the feel of the story. Much of the story was impactful; slowing down the text at the end kind of lessened the impact for me, as if the author wasn't sure that the text alone would be weighty enough. I think it was! It was also a lesson for me because I'm working on a short twine game and had imagined slowing down the most dramatic moments.
The game uses multimedia in an effective way, and overall gives off a highly polished feel. The writing is the kind I would think of if someone said 'What's an example of good writing in a recent IFComp?'