Develop a Functional Calculator Using HTML, CSS, and JavaScript

Create a calculator using HTML, CSS, and JavaScript that can perform basic and advanced mathematical operations. It should have a user-friendly interface and support real-time input validation.

### Functions to be Added

1. **Basic Operations:**
- Addition (+)
- Subtraction (-)
- Multiplication (*)
- Division (/)

2. **Advanced Functions:**
- Exponentiation (x^y)
- Square root (√x)

3. **Trigonometry:**
- sin, cos, tan
- sin⁻¹, cos⁻¹, tan⁻¹

5. **Constants & Features:**
- Pi (π)
- Euler’s number (e)

6. **User Interaction:**
- Clear (C)
- Backspace (⌫) buttons

If the user enters a value that is not valid for a function (e.g., sin⁻¹(2) or √-1), the calculator should show an error message.