Controlling service flow from the Caller method

Is it correct to control how the service works from the caller of this service? I had such a problem today, and don't know if my solution is good or not. Hope someone more advanced can give me a feedback. Here is my problem:

I have got a service with method Foo:

public class Service
{
    public int? Foo(int? number, bool throwException)
    {
        int? result = number;

        if (result == null)
        {
              var result = ...
              if (result == null && throwException)
              {
                    throw new Exception("ZZZZ");
              }
        }

        return result
    }
}

Now in Caller class I got 2 methods where I invoke this Service:

public class Caller
{
    public void Test1()
    {
        ...         
        Service.Foo(number, TRUE);
        ...
    }

    public void Test2()
    {
        ...         
        Service.Foo(number, FALSE);
        ...
    }

As you can see for Test1 im sending flag throwException TRUE, and for Test2 FALSE, is it good practice to control how the Service's flow go from the Caller's methods?