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class Layer:
    """Implement a class for a neural network layer.

    The class should implement the forward and backward passes of the layer.
    """

    def __init__(self):
        """Implement the initialization of the layer parameters.

        Arguments:
        None

        Returns:
        None
        """

        # Parameters of the layer. Should be initialized randomly.
        self.w = np.random.randn()
        self.b = np.random.randn()

        # Activation function for the layer.
        self.activation = relu
        self.activation_derivative = relu_derivative

        # Attributes to store the input and output of a layer during forward pass, for use in the backward passes.
        self.last_x = None
        self.last_a = None

    def forward(self, x):
        """Implement the forward pass of the layer.

        Arguments:
        x - the input to the layer, scalar of type 'float'

        Returns:
        a - the output of the layer, scalar of type 'float'
        """
        # Compute the linear transformation
        a = self.w * x + self.b

        # Store the input and output for the backward pass
        self.last_x = x
        self.last_a = a

        return a

    def backward(self, de_da, step_size=0.01):
        """Implement the backward pass of the layer. The backward pass should update the parameters of
        the layer and return the derivative of the error with respect to the input of the layer.

        Arguments:
        de_da - the derivative of the error with respect to the output of the layer, scalar of type 'float'
        step_size - the step size for the update step, scalar of type 'float'

        Returns:
        de_dx - the derivative of the error with respect to the input of the layer, scalar of type 'float'
        """
        # Compute the gradient with respect to w, b, and x
        dw = de_da * self.last_x  # Derivative w.r.t. w
        db = de_da  # Derivative w.r.t. b
        de_dx = de_da * self.w  # Derivative w.r.t. input x

        # Update weights and biases
        self.w -= step_size * dw
        self.b -= step_size * db
        return de_dx