input: def train_mnist_model(learning_rate: float, training_epochs: int, batch_size: int) -> float:
      """Trains a neural network model using TensorFlow to classify hand-written digits from the MNIST dataset.
      Returns the accuracy of the model on the test set.
      
      >>> train_mnist_model(0.001, 15, 100)
      0.9234
      """
output:     
      import tensorflow as tf
      from tensorflow.keras import layers, models
      from tensorflow.keras.datasets import mnist
      from tensorflow.keras.utils import to_categorical
  
      # Load and preprocess the MNIST dataset
      (x_train, y_train), (x_test, y_test) = mnist.load_data()
      x_train = x_train.reshape((x_train.shape[0], 28, 28, 1)).astype('float32') / 255
      x_test = x_test.reshape((x_test.shape[0], 28, 28, 1)).astype('float32') / 255
      y_train = to_categorical(y_train)
      y_test = to_categorical(y_test)
  
      # Build the model
      model = models.Sequential([
          layers.Conv2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)),
          layers.MaxPooling2D((2, 2)),
          layers.Conv2D(64, (3, 3), activation='relu'),
          layers.MaxPooling2D((2, 2)),
          layers.Conv2D(64, (3, 3), activation='relu'),
          layers.Flatten(),
          layers.Dense(64, activation='relu'),
          layers.Dense(10, activation='softmax')
      ])
  
      # Compile the model
      model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=learning_rate),
                    loss='categorical_crossentropy',
                    metrics=['accuracy'])
  
      # Train the model
      model.fit(x_train, y_train, epochs=training_epochs, batch_size=batch_size, verbose=0)
  
      # Evaluate the model on the test set
      test_loss, test_accuracy = model.evaluate(x_test, y_test, verbose=0)
  
      return test_accuracy
  