I'm finding myself falling into the trap of memorizing some sort of cookbook recipes in calculus class instead of using my brain. I'd really like to find some conceptually challenging calculus 1 (freshman undergrad) problems to break this. The problem is that the "challenge problems" in pretty much any textbook I've found are just really tedious calculations or algebraic manipulations, aka "number crunching".
Thus, I'm looking for some sort of book or website (preferably with answers) that had truly creative, stroke-of-genius required calculus problems.
To further refine what I'm looking for, I'll add that the problems:
shouldn't be just asking for a proof. I have no idea how to even go about a formal proof. (learning this is a separate quest)
shouldn't require any theorems or facts outside of a pure math freshman calculus course (like some weird law of physics or statistics).
shouldn't require overly complicated integration or derivative formulas. I'll probably just crunch any resulting equations with Wolfram Alpha.
isn't just a very long problem asking to find 75 different things from 75 unsightfull equations.
doesn't ask me to hand-draw some stupid graph.
I've had some minor success in learning how to think more in depth by reading very old calculus books from like 1962, but they either don't have practice problems or keep asking me to write proofs or do something super mathematically rigorous. I'm really more after a brain-teaser puzzle...but that works my calculus muscles a bit more.