optuna/optuna-examples ? reverse-engineered prompt

Build me a Python examples repository for Optuna that shows how to use it in lots of real world machine learning cases.

I want a simple README and a set of small runnable example scripts that cover basic optimization, multi objective optimization, pruning, samplers, visualization, and distributed runs. It should include examples for common tools like scikit learn, PyTorch, TensorFlow, LightGBM, XGBoost, CatBoost, Keras, and a few distributed setups like Dask, Ray, and Kubernetes. A quickstart notebook would be great too.

Keep the examples easy to follow and focused on helping someone try Optuna on their own project, not on building a full app. If you need to check the latest Optuna docs while wiring up the examples, go ahead and look them up online. Make sure each example is small, clear, and actually runs without a lot of setup.