**Core Concept**
The sciatic nerve is a major nerve in the lower limb that arises from the L4-S3 nerve roots. It divides into two main branches: the tibial nerve and the common peroneal nerve. The tibial nerve is responsible for innervating the posterior compartment muscles of the thigh and the muscles of the posterior compartment of the leg.

**Why the Correct Answer is Right**
The muscles of the posterior compartment of the leg, including the gastrocnemius, soleus, and plantaris, are primarily innervated by the tibial nerve. This is due to the fact that the tibial nerve arises from the sciatic nerve and courses down the posterior aspect of the leg, providing motor innervation to these muscles. The tibial nerve also provides sensory innervation to the skin of the sole of the foot.

**Why Each Wrong Option is Incorrect**
* **Option A:** The quadriceps femoris muscle is actually innervated by the femoral nerve, not the tibial nerve. The femoral nerve arises from the L2-L4 nerve roots and is responsible for innervating the anterior compartment muscles of the thigh.
* **Option B:** The flexor hallucis longus muscle is a deep muscle of the posterior compartment of the leg and is innervated by the tibial nerve. This muscle is responsible for flexion of the great toe.
* **Option C:** The flexor digitorum longus muscle is a deep muscle of the posterior compartment of the leg and is innervated by the tibial nerve. This muscle is responsible for flexion of the toes.

**Clinical Pearl / High-Yield Fact**
The tibial nerve is often affected in conditions such as tarsal tunnel syndrome, where compression of the nerve leads to pain and paresthesias in the foot. It is essential to recognize the symptoms and signs of tibial nerve compression to provide appropriate treatment and management.

**Correct Answer: A. Quadriceps femoris muscle**