LINQ to Entities does not recognize the method 'Int32 Parse(System.String)' method, and this method cannot be translated into a store expression

in Linq to Entity, you should use the methods in your query which is supported by your provider to convert them to expression tree to run on your Data Base side.

all providers must support some methods by default called Canonical Functions (Read More Here), and also you can define your user defined function and stored procedure as edm functions to use in linq query (Read More Here) and (Here).

in addition you can use methods which is supported by providers and can be converted to expression tree which are in EntityFunctions and SqlFunctions.

and finally about your question, you can convert UserID and ClassID before your query, like this:

var UID = int.Parse(UserID);
var CID = int.Parse(ClassID);
var record = context.enrollments.SingleOrDefault
    (row => row.userId == UID && row.classId == CID);