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def deduplicate_lines(text: str, case_sensitive: bool = True) -> str:
    """Remove duplicate lines from text, preserving order of first occurrence."""
    lines = text.splitlines()
    seen = set()
    unique_lines = []

    for line in lines:
        key = line if case_sensitive else line.lower()
        if key not in seen:
            seen.add(key)
            unique_lines.append(line)

    return "\n".join(unique_lines)

# Example usage
text = """apple
banana
apple
cherry
BANANA
banana"""

print(deduplicate_lines(text))
# apple
# banana
# cherry
# BANANA

print(deduplicate_lines(text, case_sensitive=False))
# apple
# banana
# cherry