No, 6.03 is not within most lab's ranges. Typical ranges are 0.3-3.0, 0.4-4.50, 0.5 -5.0 or something along those lines. Depending on age, some doctors believe that anything under 10 is satisfactory - it's not. A result of 6.03 indicates hypothyroidism.
It's important to note that TSH is a pituitary hormone and in spite of doctors believing it's all that's needed to determine thyroid status, it should never be used as the sole diagnostic test for a thyroid condition.
What, if any symptoms do you have?
When you talk to your doctor, ask for Free T4 and Free T3. If you just ask for T4 and T3, you will get tests for the Total amounts of each and that's not adequate.