[Minor spoilers for regular and secret encounters on a normal route, and answers to the calculus challenge:]
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(incomplete) List of "Secrets":
Secret Concept: Sigma Sum
Edit: As mopedmorning commented, when you get to the Exponents dialogue with three choices including [yea, I also think so.], choose that one and he'll tell you about dating Logarithms. This unlocks the following steps.
When you're near the end of the date with trigonometry and get to the [*silence*] vs. [yes. yes. yes.] dialogue option, choose [*silence*] and rizz trizz will give you a [Sine Flower]. Later during the date with Logarithms when they're crying over Exponents, you can give them the flower as a gift for Exponents and they will get back together :) Doing so will grant you a secret encounter with Sigma Sum.
Calculus Challenge Answers (please check for mistakes, might've gotten one wrong and maybe they still counted that as a pass lol):
1. (e^6 - 1)/2
2. f has a relative maximum at x=1
3. 1/2
4. 98/3
5. y = 4 + 2e^(x^3)
6. Conditionally convergent only
7. 3
8. (MY BAD THIS ONE DOES MATTER) 1. don't pick 2.
Secret Concept: Graphing Calculator
Passing the Calculus Challenge will grant you a secret encounter with Graphing Calculator, who gives you a hint on how to start the genocide route (though the name makes it pretty obvious lol).
Secret Concept: Mysterious Monolith (Euler's Identity)
When Möbius Strip offers you a drink, choose [yes.] and he will give you the [Gintegral]. Later you can offer the bottle to Alexandria and she'll drop a giant rectangular monolith on Equality when he comes to weigh your heart. This gives you a secret encounter with the Mysterious Monolith.
Secret Concept: XYZ
If you kill Ms. Fibonacci / Golden Spiral (you monster) she will drop the [Apollonian Gasket]. During your conversation with Sierpiński Triangle he will ask you to hand it over. If you agree, you will later get a secret encounter with XYZ.
Edit: This was found by SirMadam in the comments! Secret Concept: Yellow Pig
When you get to Hilbert's Hotel and are prompted to choose a room, put 17 in the text box. You will later get a secret encounter with Yellow Pig.
And that's all(?) the secret encounters accessible in a normal route! For content in Endings 2-4... check out the other [SPOILERS] community posts :]