Programming Challenges - Increasing Difficulty

Task 1: Basic Plotting
Create a Python script that plots a simple quadratic function y = x^2 for x values from -5 to 5.
Requirements:
- Use NumPy to generate the x values (at least 100 points)
- Calculate corresponding y values
- Plot the function using Matplotlib
- Add appropriate labels and title

Task 2: Multiple Functions
Extend your script to plot two functions on the same graph:
- y1 = sin(x)
- y2 = cos(x)
Requirements:
- Plot both functions for x values from 0 to 4π
- Use different colors for each function
- Add a legend to distinguish the functions
- Include axis labels and a title

Task 3: Parametric Plotting
Create a script that plots a parametric curve (e.g., a spiral or Lissajous figure).
Requirements:
- Use parametric equations to generate x and y coordinates
- Plot the curve with appropriate styling
- Add labels, title, and grid
- Experiment with different parameter ranges

Task 4: Data Visualization
Create a script that visualizes a dataset (you can generate synthetic data or use built-in datasets).
Requirements:
- Create at least 2 different types of plots (e.g., line plot, scatter plot, bar chart)
- Include proper labels, titles, and legends
- Use color effectively to enhance understanding
- Add annotations or special markers for important data points

Task 5: Interactive Plotting
Create an interactive plot where users can modify parameters and see the results in real-time.
Requirements:
- Use matplotlib widgets or another interactive library
- Allow users to change at least 2 parameters of a function
- Update the plot dynamically as parameters change
- Include clear instructions for the user

Task 6: Advanced Visualization
Create a comprehensive visualization that combines multiple plot types in subplots.
Requirements:
- Create at least 3 subplots with different types of visualizations
- Share axes where appropriate
- Use consistent styling across all subplots
- Include a main title for the entire figure
- Save the figure to a file with high resolution

Task 7: Object-Oriented Plotting
Refactor one of your previous scripts to use object-oriented Matplotlib approach.
Requirements:
- Use Figure and Axes objects explicitly
- Create reusable plotting functions or classes
- Implement proper error handling
- Document your code with comments or docstrings

Task 8: Custom Visualization
Create a unique visualization of your choice that demonstrates advanced Matplotlib features.
Requirements:
- Use advanced features like custom colormaps, 3D plotting, or animations
- Include data analysis or transformation
- Make the visualization informative and visually appealing
- Provide a clear explanation of what the visualization shows