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Minimum Product from Tuple Pairs

Write a Python function `min_product_tuple` that takes a list of tuples as input. Each tuple contains two integers. The function should calculate the product of the two integers in each tuple and return the smallest product among all the tuples.

#### Example Usage
```python [main.nopy]
print(min_product_tuple([(2, 7), (2, 6), (1, 8), (4, 9)]))  # Output: 8
print(min_product_tuple([(10, 20), (15, 2), (5, 10)]))      # Output: 30
print(min_product_tuple([(11, 44), (10, 15), (20, 5), (12, 9)]))  # Output: 100
```

#### Constraints
- The input list will contain at least one tuple.
- Each tuple will contain exactly two integers.
- The integers can be positive, negative, or zero.
def min_product_tuple(list_of_tuples):
    """
    Calculate the minimum product from pairs of tuples in a list.

    Args:
        list_of_tuples (list): A list of tuples, where each tuple contains two integers.

    Returns:
        int: The smallest product among all tuple pairs.
    """
    # Placeholder for the solution
    pass
Intermediate functionslistsmath
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