Faith does not mean belief without evidence, it is more belief in something not seen. That does not imply a lack of evidence.
For example, you have faith in the efficacy of a pharmaceutical product based on the fact that you trust the peer reviewers of the reports of its clinical trials, and the reputation of the journals those reports are published in.
Without faith you could not accept any scientific conclusion unless you had directly observed the experiments they were based on. Neither could you believe anything on the news or any historical event you hadn't observed.
You might be arguing semantics, but I'm not. I see a gulf of difference between any definition of "faith" and how I derive confidence in science.
No definition of faith I'm aware of relates to confidence based on weight of evidence, or balance of probabilities.
To use your example of pharmaceutical efficacy, I take a pill with the expectation that it will elicit results comparable to its stated claim. I hope that it works. I'm happy if it does work. But my worldview won't be shattered if it doesn't.
There's pretty-good-guess faith and blind faith. Mathematical axioms and believing what other people tell you about science you haven't observed yourself are examples of the former. Belief in God varies between the two from person to person.
There's a way of formalizing this, so we don't have to rely on the imprecise and loaded word "faith": Bayesian probability, e.g. as described on http://lesswrong.com. See also http://rationality.org.
For example, you have faith in the efficacy of a pharmaceutical product based on the fact that you trust the peer reviewers of the reports of its clinical trials, and the reputation of the journals those reports are published in.
Without faith you could not accept any scientific conclusion unless you had directly observed the experiments they were based on. Neither could you believe anything on the news or any historical event you hadn't observed.