Sure, I can help you write a test case generator for the problem "Mobile Computing." Here is a Python script that generates random test cases for this problem:

```python
import random

def generate_test_case():
    # Number of datasets (randomly chosen between 1 to 5 for simplicity)
    num_datasets = random.randint(1, 5)
    
    test_cases = []
    
    for _ in range(num_datasets):
        # Room width (random float between 0 and 10)
        r = round(random.uniform(0.00001, 9.99999), 5)  # using 5 decimal places for precision
        
        # Number of stones (between 1 and 6)
        s = random.randint(1, 6)
        
        # Weights of the stones (between 1 and 1000)
        weights = [random.randint(1, 1000) for _ in range(s)]
        
        test_cases.append((r, s, weights))
    
    return num_datasets, test_cases

def format_test_case(num_datasets, test_cases):
    result = [str(num_datasets)]
    for r, s, weights in test_cases:
        result.append(f"{r}")
        result.append(f"{s}")
        result.extend(map(str, weights))
    return "\n".join(result)

def tcgen():
    num_datasets, test_cases = generate_test_case()
    return format_test_case(num_datasets, test_cases)

# Example of generating a test case
print(tcgen())
```

### Explanation:

1. **generate_test_case Function**:
   - Generates the number of datasets (`num_datasets`), which is a random integer between 1 and 5.
   - For each dataset:
     - Generates a random room width `r` as a float between 0.00001 and 9.99999, rounded to 5 decimal places.
     - Generates a random number of stones `s` between 1 and 6.
     - Generates a list of stone weights, each a random integer between 1 and 1000.

2. **format_test_case Function**:
   - Formats the generated test cases into the required input format for the problem statement.
   - Combines all the parts into a single string suitable for competitive programming input.

3. **tcgen Function**:
   - Calls the above functions to generate and format the test cases, then simply prints the result.

You can run this script to get a random test case each time. It ensures the test cases conform to the constraints specified in the problem statement.