There are repeated references in Daniel to knowledge of the world being a blessing from God. Likewise, Colossians 2:3 speaks of Christ "in whom are hid all the treasures of wisdom and knowledge". However, 1 Timothy 6: 2 contains a warning about the opposition of "science so called," or in other words, incorrect knowledge that claims authority but contradicts revealed truth.
Scientific investigation has shown that the world around us works according to consistent laws, which is very much in keeping with what we know of God as a God of order, and there is much benefit to be found in learning about the rules that He set up. But it's important to keep in mind that science is only based on observation and investigation, and trying to reverse-engineer the nature of the rules from the results we can observe, and thus the actual "scientific truth" about certain things tends to change as they become more fully understood. (For some interesting reading on the subject, do a bit of research on the history of the Cosmological Constant.) When current scientific understanding conflicts with revealed truth, it's likely that someone didn't quite get their experiment right.
It's also important to keep in mind that not all things that are believed or taught by religious leaders are actually based in revealed truth. One of the obvious examples would be the medieval Catholic Church's persecution of Copernicus for his scientific notions about the nature of the Solar System. This knowledge contradicted dogmatic notions held by the Church that have no actual basis in the Bible, but instead derive from Greek philosophy and got incorporated into the dogma back when the Church was the state religion of the Roman Empire.
And finally, it's important to remember that scientists are human too. They occasionally have an agenda beyond simply furthering the spread of knowledge of how the world works. Experiments don't lie, but experimenters sometimes do.
I believe that God is a God of order, and that there is no conflict between true science and true religion, but that for various reasons sometimes non-true versions of both science and religion do spring up and gain widespread popularity and acceptance. If you run into something claiming scientific authority that contradicts your religious beliefs, then one or the other (or possibly both) is in error. Reason about it, try to find an explanation that makes sense, then pray about it and ask God if you've reached the right conclusions. He won't steer you wrong, even if other authorities do.