input: 
  def predict_stock_market_movements(data: pd.DataFrame) -> float:
      """ Predict stock market movements using a deep learning model. 
      The function takes a pandas DataFrame as input, where the first column 
      is the independent variable and the second column is the dependent variable.
      The function returns the mean squared error of the model's predictions.
  
      >>> data = pd.DataFrame({
      ...     'independent': [1, 2, 3, 4, 5],
      ...     'dependent': [1, 4, 9, 16, 25]
      ... })
      >>> predict_stock_market_movements(data)
      0.0
      """
      
      #split data into train and test data
      X_train = data.iloc[:, 0] #Choosing the independent variable 
      y_train = data.iloc[:, 1]  #Choosing the dependent variable
      X_test = data.iloc[:, 0] #Choosing the independent variable 
      y_test = data.iloc[:, 1]  #Choosing the dependent variable
      
      #Build a deep learning model
      import tensorflow as tf
      from tensorflow.keras.layers import Dense
      from tensorflow.keras.models import Sequential
      
      #create a model and add layers
      model = Sequential()
      model.add(Dense(64, input_shape=(1,), activation='relu'))
      model.add(Dense(128, activation='relu'))
      model.add(Dense(64, activation='relu'))
      model.add(Dense(1))
      
      #compile the model
      model.compile(optimizer='adam', loss='mse', metrics=['mse'])
      
      #train the model
      model.fit(X_train, y_train, batch_size=64, epochs=20, validation_data=(X_test, y_test))
      
      #Evaluate the model
      score = model.evaluate(X_test, y_test, verbose=0)
      return score[1]
  
output:     predictions = model.predict(X_test)
      mse = ((predictions - y_test) ** 2).mean()
      return mse