Sure, I'll write a test case generator for the given problem statement. This generator will create various valid expressions in the Shipura language and ensure the inputs cover different edge cases and complexities.

Here's the Python code for the test case generator:

```python
import random

def generate_number():
    return str(random.randint(0, 1_000_000_000))

def generate_expr(depth=0):
    if depth > 5 or random.random() < 0.3:
        # Generate a terminal expression (number or S<expr>)
        if random.random() < 0.5:
            # Generate a number
            return generate_number()
        else:
            # Generate a S<expr>
            return f"S< {generate_expr(depth + 1)} >"
    else:
        # Generate a composite expression (expr >> term)
        return f"{generate_expr(depth + 1)} >> {generate_term(depth + 1)}"

def generate_term(depth=0):
    if random.random() < 0.5:
        return generate_number()
    else:
        return f"S< {generate_expr(depth + 1)} >"

def tcgen():
    test_cases = []
    for _ in range(random.randint(1, 100)):
        expr = generate_expr()
        test_cases.append(expr)
    
    test_cases.append("#")
    return test_cases

# Example usage
if __name__ == "__main__":
    test_cases = tcgen()
    for case in test_cases:
        print(case)
```

### Explanation:

1. **generate_number()**:
   - Generates a random number between 0 and 1,000,000,000.

2. **generate_expr(depth=0)**:
   - Recursively generates an expression. If the recursion depth exceeds 5 or a random threshold is met, it generates a terminal expression (either a number or `S<expr>`).
   - Otherwise, it generates a composite expression `expr >> term`.

3. **generate_term(depth=0)**:
   - Generates a terminal term (either a number or `S<expr>`).

4. **tcgen()**:
   - Calls `generate_expr()` to create expressions.
   - Appends the terminating `#` to signal the end of the input.

This generator creates a diverse set of test cases of varying complexity, ensuring that the expressions are valid according to the Shipura language syntax.