Religion and science are not opposed. Claiming otherwise comes, at the very least, as not well informed.
Sorry to nitpick, but science isn't verifiable, it's falsifiable. Also, there are religious people who'd agree with your characterisation of faith and there are others who wouldn't.
If you want it in an academic sense, then you could say that authentic biblical faith is always on the basis of the historical method.
For example, see Luke writing to Theopilus:
"Inasmuch as many have undertaken to compile a narrative of the things that have been accomplished among us, just as those who from the beginning were eyewitnesses and ministers of the word have delivered them to us, it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, that you may have certainty concerning the things you have been taught."
And see Paul writing to the early Corinthian church:
"And if Christ has not been raised, then our preaching is in vain and your faith is in vain."
"Faith is the assurance of things hoped for, the conviction of things not seen" (Catechism of the Catholic Church.)
Which is exactly what science is not.
And if all your faith and your preaching depends on the actual historicity of an impossible event, to which you seek no further explanation than something equivalent to "it's magic" (and no further interpretation but "then it means we're right"!), then of course this attitude is very far from being compatible with science.
And if it is original to Hebrews 11, then what does the phrase "assurance of things hoped for" mean in context if it does not have the same sense as 1 Corinthians 15 or Luke 1?
When you speak of "an impossible event", what do you mean exactly?
And when you say "impossible", then according to what logic?
Are you saying that it is impossible for God (should he exist) to raise the dead?
Are you saying that it is impossible for the dead to be raised because you presuppose that God does not exist?
Or are you saying that it is impossible in the sense that we have very few occurrences of such an event and therefore it must be impossible?
Well, they believe it because somebody told them to. Then, if you're asking why that formulation and not another one, then yes, it comes from Hebrews 11. But even if that passage justified the Catholic one, wouldn't that just shift the question: if they believe so and so because it comes from Hebrews 11, then why do they believe in Hebrews 11?
I mean "impossible" in natural terms, according to the believers themselves. If it were possible, but just a rare occurrence, then it wouldn't justify building a whole faith system on it, don't you agree? For a Christian the resurrection must have happened despite being impossible: the impossibility it's exactly where it derives its value from. The impossibility is cherished, treasured.
Contrast now with a scientific attitude. It has happened? Therefore it's possible and (until further understanding) it doesn't prove anything except its own possibility. And understanding means discovering the mechanical, reproducible and predictable nature of the process. Any aspect that is not mechanical, reproducible and predictable will have to be ignored by the scientific inquiry. Even if it contains the right answer.
That is not the definition of scientific inquiry, or you would be ruling out most of the sciences.
As for Hebrews 11, that chapter does in fact give examples of authentic biblical faith, as opposed to "blind faith". In other words, people (everyone from patriarchs and prophets to prostitutes) acting on the basis of what God said and did in history (often their own recent past). As a chapter by itself, Hebrews 11 is enough to show that faith is always on the basis of the historical method, not on the basis of wishful thinking. And Hebrews is not the only book in the Bible. The Bible has much to say that defines authentic faith.
To come back to the resurrection, if I understand you correctly, then you are saying that the fact of the resurrection proves its possibility (incredulous as it is) and nothing more. In other words, God himself would still have to speak to give meaning to the event of the resurrection? That is the Bible's claim. You can examine it should you choose to, on the basis of the historical method according to disciplines such as textual criticism etc. which are not opposed to scientific inquiry.
And this is all at least part of the reason why some people who took the Bible seriously, started taking the world around them seriously. That at least, is the history for founding fathers of science such as Johannes Kepler (a protégé of Melanchthon, himself a protégé of Luther).
What is your name? I am sure you would want to take science seriously. I wonder if you have ever taken the Bible as seriously, like people like Luther did? With a fresh pair of spectacles?
Of course debates can go on forever, but I think that religion and science are indeed opposed, it just happens that some individuals can do excellent science while keeping religion safely confined to a corner of their brains (and the other way round, maybe).
Religion is about faith, science is- well, not. Religion starts with believing in something without adequate proof (by definition, or it would be science). Science looks for the proof of everything. Religion searches for unexplainable things, to be used as a proof of an immutable knowledge; science searches for unxplainable things to prove that the existing knowledge is wrong, and by modifying it, make them more explainable.