How do Muslims (or Christians etc) reconcile their faith with the evidence from Science? Muslims also have problems in Western countries reconciling their faith with many of medieval punishments meted out under Islamic (Sharia) law.
If you were to ask this question of a Muslim (or anyone with strong faith in any of the major religions) they would probably respond with a denial that there is any problem at all. Denial is usually the first line of defence.
After admission that perhaps there are some areas where there is 'apparent' disagreement, the reconciliation process seems to generally take two forms: Compartmentalisation and Rationalisation. Most Muslims are subconsciously experts at both forms of defence.
If there are internal doubts or unresolved questions, they are most often simply shelved to be dealt with later (probably never) because "right now I've got something more important to do". The issues are "not that important anyway" or some authority figure (parents, teacher, Imam, Mullah, book, TV program etc) "told me it was a fact, so who am I to argue?" So the responsibility is shifted to someone else and we can get on with our lives. These are examples of denial and compartmentalisation.
It is necessary for two main reasons:
For a nice example of the contortions necessary to reconcile Evolution with the Quran, check out Dr. Yasir Quadhi in this YouTube presentation at around the 17 minute mark!
Ali Sina has nicely documented his metaphorical 'journey' from Faith to Enlightenment via seven valleys. A summary of this is shown in the diagram below. This series of transitions seems to be common among Muslims who 'see the light'.
It should be noted that the Mu'tazila Muslim Scholars back in the 8th to 10th centuries (AD) promoted a more allegorical reading of the Quran and promoted the use of reason and rational thought. Sadly this school of thought languished and suffered heavy losses under the Mihna, the Islamic inquisition launched under the Abbasid Caliph al-Ma'mun (d. 218 AH/833 AD)
While on your journey of discovery, keep an open mind and maintain a balanced judgement. Keep an awareness of the various logical fallacies that we all fall into occasionally. Look out for these during your quest for knowledge and eliminate them from your own mind. These common fallacies are detailed in books by Carl Sagan and Michael Shermer.