import json
import sys
import types
from typing import Dict, Union

def execute_python(source: str) -> Union[Dict, str]:
    """
        Evaluate a Python program and return the globals it declared.
        Can be used to compute mathematical expressions (e.g. after importing math module).

        Args:
            source: contain valid, executable and pure Python code. Should also import any required Python packages.
                For example: "import math\nresult = math.cos(2) * 10"

        Returns:
            dict | str: A dictionary containing variables declared, or an error message if an exception occurred.
    """
    namespace = {}
    sys.stderr.write(f"Executing Python program:\n{source}\n")
    exec(source, namespace)
    results = {
        k: v
        for k, v in namespace.items()
        if not k.startswith('_') and not isinstance(v, type) and not callable(v) and not isinstance(v, types.ModuleType)
    }
    sys.stderr.write(f"Results: {json.dumps(results, indent=2)}\n")

    return results