Q:

Moq and the parameters you pass

I create a MOQ object
pass it to my class
call it and pass in an object.
How can I get access to this object to see if the right properties are set?

A:

If I'm reading your question correctly you seem to have a situation like this?
public void DoTheCalculation(ICalculator calculator) {
   calculator.Calculate(this /* Or any other object */);
}

In which case you can assert upon the arguments passed to a Mocked interface using the It.Is method that accepts a predicate:
[TestMethod]
public void DoTheCalculation_DoesWhateverItShouldDo() {
     Mock<ICalculator> calcMock = new Mock<ICalculator>();
     CalculationParameters params = new CalculationParmeters(1, 2);
     params.DoTheCalculation(calcMock.Object);

     calcMock.Verify(c => c.Calculate(It.Is<CalculationParameters>(
                         c => c.LeftHandSide == 1 
                              && c.RightHandSide == 2));

}

