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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def deploy_api_gateway( self, api_id, stage_name, stage_description="", description="", cache_cluster_enabled=False, cache_cluster_size='0.5', variables=None, cloudwatch_log_level='OFF', cloudwatch_data_trace=False, cloudwatch_metrics_enabled=False, cache_cluster_ttl=300, cache_cluster_encrypted=False ):
 """ Deploy the API Gateway! Return the deployed API URL. """

        print("Deploying API Gateway..")

        self.apigateway_client.create_deployment(
            restApiId=api_id,
            stageName=stage_name,
            stageDescription=stage_description,
            description=description,
            cacheClusterEnabled=cache_cluster_enabled,
            cacheClusterSize=cache_cluster_size,
            variables=variables or {}
        )

        if cloudwatch_log_level not in self.cloudwatch_log_levels:
            cloudwatch_log_level = 'OFF'

        self.apigateway_client.update_stage(
            restApiId=api_id,
            stageName=stage_name,
            patchOperations=[
                self.get_patch_op('logging/loglevel', cloudwatch_log_level),
                self.get_patch_op('logging/dataTrace', cloudwatch_data_trace),
                self.get_patch_op('metrics/enabled', cloudwatch_metrics_enabled),
                self.get_patch_op('caching/ttlInSeconds', str(cache_cluster_ttl)),
                self.get_patch_op('caching/dataEncrypted', cache_cluster_encrypted)
            ]
        )

        return "https://{}.execute-api.{}.amazonaws.com/{}".format(api_id, self.boto_session.region_name, stage_name)