As promised, here is the list of some first year calculus problems collections:
– MAA Notes series. Resources for Calculus Collection, Volume 2: Calculus Problems for a new century, Robert Fraga, Editor
– Shell Centre for Mathematical Education, Publications https://www.mathshell.com/index.php
– Math Problems Database, http://bfc.sfsu.edu/cgi-bin/prob.pl
(hard problems solved in groups, as in the Emerging Scholar Program)
And some people, like Featherstone et. al.  and Schoenfeld , have described “good problems” as being accessible, having multiple solution paths that promote establishing mathematical connections, introducing the learner to big mathematical ideas, and being extensible to further exploration. Also, tasks in which students are asked to give examples of their own or explain some nontrivial mathematics to peers have often been used.
 Featherstone, H., Crespo, S., Jilk, L.M., Oslund, J.A., Parks, A.N., & Wood, M. B. (2011) Smarter together! collaboration and equity in the elementary math classroom. Reston, VA: National Council of Teachers of Math- ematics.
 Schoenfeld, A.H. (1991). “What’s all the fuss about problem solving?”. Zentralblatt fur Didaktik der Mathematik, 91 pp. 4-8