http://www.pewforum.org/2013/04/30/...ligion-politics-society-beliefs-about-sharia/
Muslims also tend to believe sharia has only one, true understanding, but this opinion is far from universal; in some countries, substantial minorities of Muslims believe sharia should be open to multiple interpretations.
Although many Muslims around the world say sharia should be the law of the land in their country
[my addition: many Christians throughout the world believe this in regards to their rules], the survey reveals divergent opinions about the precise application of Islamic law.
14 Generally, supporters of sharia are most comfortable with its application in cases of family or property disputes. In most regions, fewer favor other specific aspects of sharia, such as cutting off the hands of thieves and executing people who convert from Islam to another faith.
...
In 17 of the 23 countries where the question was asked, at least half of Muslims say sharia is the revealed word of God.
Muslims in Southeast Asia and Central Asia are somewhat less likely to say sharia comes directly from God.
...
Muslims differ widely as to whether sharia should be open to multiple understandings. While many say there is only one true interpretation, substantial percentages in most countries either say there are multiple interpretations or say they do not know.
In a number of countries, significant percentages say they are unsure whether sharia should be subject to one or multiple understandings,
...
Support for making sharia the official law of the land varies significantly across the six major regions included in the study.
...
Among Muslims who support making sharia the law of the land, most do not believe that it should be applied to non-Muslims.
...
Compared with attitudes toward applying sharia in the domestic or criminal spheres, Muslims in the countries surveyed are significantly less supportive of the death penalty for converts.
And here are some of the charts:
So, as you can see, although Sharia is believed in, it's exact belief and interpretation widely varies.