Putting it in hide tags because well, its sort of on-topic but in such a generalized way its borderline off-topic and its a big wall of text.

Actually, faith means to believe in something not only without proof, but not actually looking for proof, and is actually valued by the lack of proof, or better, by having strong evidence AGAINST it.
I cant think of a non religious example of it honestly... Faith as a term is often used in other contexts like saying I HAVE FAITH IN YOU HARRY, but this is not actual faith, as its usually because this HARRY person is very courageous and stuff, so you actually have evidence that suggests your "faith" is well placed. If you place faith in the work of a scientist, you obviously have reasons to (if hes not just anyone who called himself "scientist" and wrote a book, in this case it is a straw man argument)
Now the dictionary definitions pretty much takes in all of these uses of the word, but if you take it at such a large definition, the word becomes pretty much just a synonym of "view" so it loses all meaning to this debate.)

What could be seen as "faith" though, would be to have in front of you two possible explanations for one phenomena, and hold one of the two to be your favorite, with no actual evidence favoring it (or worse with evidence disproving or ridiculing your own) or otherwise influencing your choice. That here could be considered as "faith" in a theory over another. Its still not exactly like religious faith though, because its not valued by how little evidence there is, here the evidence against the held theory is just disregarded, and the evidence backing it up is overvalued. Its still kind of faith though.

But other than this, there isn't such a thing as "faith" as far as science goes. For instance, saying that unicorns don't exist isn't faith, since there is evidence to the idea they don't exist (we never saw any). its not a fact either, because setting it as a fact would require us to look into the whole universe and make sure there aren't unicorns anywhere (and even there one could argue that we just cant see them but they're still all over the place, blah blah).
Saying that they exist though, IS faith. See, its not because two ideas are conflicting and that one of them is faith-based, that the other must be faith based also. That said, maybe unicorns do exist, but no matter what the truth ultimately is, whether something is based on faith or not depends entirely on the evidence we have right now, and well, the evidence point that they don't.

You could also argue that you cannot trust what a book says unless you do the tests yourself, so just assuming the book is not lying or misguiding you is faith in itself, but this is a dangerous slope to debate into. after you do the tests yourself, what proves you some evil scientist didn't mess with your results!? And maybe your senses lied to you, too! In the end you could end with Descartes-like things where nothing is to be considered fact because you cant truly prove anything other than your own existence blah blah blahbnlahblahbah.