📝 **Task:** Implement `estimate(input_fresh, input_cached, output, price_in, price_out, batch=False) -> float`. Rules: * Fresh input tokens cost `price_in` per 1M. * Cached input tokens cost `0.1 * price_in` per 1M (10%). * Output tokens cost `price_out` per 1M. * If `batch=True`, multiply the whole thing by `0.5`. * Round result to 4 decimals. The driver exercises four scenarios: canonical sync, same batched, all-fresh (no cache benefit), and zero-output (input-only cost). Expected output: ``` sync=0.0132 batch=0.0066 no_cache=0.0375 no_output=0.0057 ``` 📋 Implement the function above. Tests run automatically. 💡 **Hint:** Re-read the theory if stuck.