PyQt5 ошибка AtributeError: 'Ui_TaskWindow_1' object has no atribute 'ContentsButton'

Первое, что вы должны запомнить - НИКОГДА НЕ изменяйте модуль созданный в QT Designer. НИКОГДА.

Вы должны воспринимать этот модуль как файл ресурсов.

Создайте класс и наполните его тем что вы создали в QT Designer.

main.py

from PyQt5 import QtCore, QtGui, QtWidgets
from TaskWindow1 import  Ui_TaskWindow_1                                   # +

class Ui_ContentsMenu(object):
    def setupUi(self, ContentsMenu):
        ContentsMenu.setObjectName("ContentsMenu")
        ContentsMenu.resize(649, 481)
        self.centralwidget = QtWidgets.QWidget(ContentsMenu)
        self.centralwidget.setObjectName("centralwidget")
        self.gridLayoutWidget = QtWidgets.QWidget(self.centralwidget)
        self.gridLayoutWidget.setGeometry(QtCore.QRect(30, 120, 301, 261))
        self.gridLayoutWidget.setObjectName("gridLayoutWidget")
        self.gridLayout = QtWidgets.QGridLayout(self.gridLayoutWidget)
        self.gridLayout.setContentsMargins(0, 0, 0, 0)
        self.gridLayout.setObjectName("gridLayout")
        self.pushButton_3 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton_3.setObjectName("pushButton_3")
        self.gridLayout.addWidget(self.pushButton_3, 0, 0, 1, 1)
        self.pushButton_2 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton_2.setObjectName("pushButton_2")
        self.gridLayout.addWidget(self.pushButton_2, 2, 0, 1, 1)
        self.pushButton = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton.setObjectName("pushButton")
        self.gridLayout.addWidget(self.pushButton, 1, 0, 1, 1)
        self.pushButton_4 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton_4.setObjectName("pushButton_4")
        self.gridLayout.addWidget(self.pushButton_4, 0, 1, 1, 1)
        self.pushButton_5 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton_5.setObjectName("pushButton_5")
        self.gridLayout.addWidget(self.pushButton_5, 1, 1, 1, 1)
        self.pushButton_6 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.pushButton_6.setObjectName("pushButton_6")
        self.gridLayout.addWidget(self.pushButton_6, 2, 1, 1, 1)
        self.label = QtWidgets.QLabel(self.centralwidget)
        self.label.setGeometry(QtCore.QRect(200, 20, 261, 71))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(14)
        self.label.setFont(font)
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        self.label.setObjectName("label")
        self.label_2 = QtWidgets.QLabel(self.centralwidget)
        self.label_2.setGeometry(QtCore.QRect(410, 180, 171, 71))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(14)
        self.label_2.setFont(font)
        self.label_2.setText("")
        self.label_2.setAlignment(QtCore.Qt.AlignCenter)
        self.label_2.setObjectName("label_2")
        ContentsMenu.setCentralWidget(self.centralwidget)
        self.menubar = QtWidgets.QMenuBar(ContentsMenu)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 649, 21))
        self.menubar.setObjectName("menubar")
        ContentsMenu.setMenuBar(self.menubar)
        self.statusbar = QtWidgets.QStatusBar(ContentsMenu)
        self.statusbar.setObjectName("statusbar")
        ContentsMenu.setStatusBar(self.statusbar)
        self.retranslateUi(ContentsMenu)
        QtCore.QMetaObject.connectSlotsByName(ContentsMenu)
#        self.pushButton_3.clicked.connect(self.gototask1)

    def retranslateUi(self, ContentsMenu):
        _translate = QtCore.QCoreApplication.translate
        ContentsMenu.setWindowTitle(_translate("ContentsMenu", "MainWindow"))
        self.pushButton_3.setText(_translate("ContentsMenu", "Task 1"))
        self.pushButton_2.setText(_translate("ContentsMenu", "Task 3"))
        self.pushButton.setText(_translate("ContentsMenu", "Task 2"))
        self.pushButton_4.setText(_translate("ContentsMenu", "Task 4"))
        self.pushButton_5.setText(_translate("ContentsMenu", "Task 5"))
        self.pushButton_6.setText(_translate("ContentsMenu", "Task 6"))
        self.label.setText(_translate("ContentsMenu", "Contents Table"))


class TaskWindow_1(QtWidgets.QMainWindow, Ui_TaskWindow_1):                       # +++
    def __init__(self, parent=None):
        super().__init__(parent)
        
        self.setupUi(self)
        

class MainWindow(QtWidgets.QMainWindow, Ui_ContentsMenu):                         # +++
    def __init__(self, parent=None):
        super().__init__(parent)
        
        self.setupUi(self)
        self.pushButton_3.clicked.connect(self.gototask1)
        
    def gototask1(self):
        self.taskWindow1 = TaskWindow_1()                              # Ui_TaskWindow_1()
        self.taskWindow1.ContentsButton.clicked.connect(self.gotomaim)  
        self.taskWindow1.show()
        self.hide()

    def gotomaim(self):
        self.show()
        self.taskWindow1.hide()        


if __name__ == "__main__":
    import sys
    app = QtWidgets.QApplication(sys.argv)
#    ContentsMenu = QtWidgets.QMainWindow()
#    ui = Ui_ContentsMenu()
#    ui.setupUi(ContentsMenu)
#    ContentsMenu.show()
    w = MainWindow()    
    w.show()
    sys.exit(app.exec_())

TaskWindow1.py

from PyQt5 import QtCore, QtGui, QtWidgets

class Ui_TaskWindow_1(object):
    def setupUi(self, TaskWindow_1):
        TaskWindow_1.setObjectName("TaskWindow_1")
        TaskWindow_1.resize(689, 456)
        self.centralwidget = QtWidgets.QWidget(TaskWindow_1)
        self.centralwidget.setObjectName("centralwidget")
        self.label = QtWidgets.QLabel(self.centralwidget)
        self.label.setGeometry(QtCore.QRect(30, 30, 351, 71))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(12)
        self.label.setFont(font)
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        self.label.setObjectName("label")
        self.VideoButton = QtWidgets.QPushButton(self.centralwidget)
        self.VideoButton.setGeometry(QtCore.QRect(380, 50, 141, 31))
        font = QtGui.QFont()
        font.setUnderline(True)
        self.VideoButton.setFont(font)
        self.VideoButton.setObjectName("VideoButton")
        self.QuestionLabel_1 = QtWidgets.QLabel(self.centralwidget)
        self.QuestionLabel_1.setGeometry(QtCore.QRect(30, 120, 191, 41))
        self.QuestionLabel_1.setObjectName("QuestionLabel_1")
        self.gridLayoutWidget = QtWidgets.QWidget(self.centralwidget)
        self.gridLayoutWidget.setGeometry(QtCore.QRect(20, 160, 131, 131))
        self.gridLayoutWidget.setObjectName("gridLayoutWidget")
        self.gridLayout = QtWidgets.QGridLayout(self.gridLayoutWidget)
        self.gridLayout.setContentsMargins(0, 0, 0, 0)
        self.gridLayout.setObjectName("gridLayout")
        self.AnswerButton_1_2 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.AnswerButton_1_2.setObjectName("AnswerButton_1_2")
        self.gridLayout.addWidget(self.AnswerButton_1_2, 1, 0, 1, 1)
        self.AnswerButton_1_3 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.AnswerButton_1_3.setObjectName("AnswerButton_1_3")
        self.gridLayout.addWidget(self.AnswerButton_1_3, 2, 0, 1, 1)
        self.AnswerButton_1_1 = QtWidgets.QPushButton(self.gridLayoutWidget)
        self.AnswerButton_1_1.setObjectName("AnswerButton_1_1")
        self.gridLayout.addWidget(self.AnswerButton_1_1, 0, 0, 1, 1)
        self.AnswerLabel_1 = QtWidgets.QLabel(self.centralwidget)
        self.AnswerLabel_1.setGeometry(QtCore.QRect(190, 190, 121, 41))
        font = QtGui.QFont()
        font.setFamily("Arial")
        self.AnswerLabel_1.setFont(font)
        self.AnswerLabel_1.setText("")
        self.AnswerLabel_1.setAlignment(QtCore.Qt.AlignCenter)
        self.AnswerLabel_1.setObjectName("AnswerLabel_1")
        self.gridLayoutWidget_2 = QtWidgets.QWidget(self.centralwidget)
        self.gridLayoutWidget_2.setGeometry(QtCore.QRect(350, 160, 185, 161))
        self.gridLayoutWidget_2.setObjectName("gridLayoutWidget_2")
        self.gridLayout_2 = QtWidgets.QGridLayout(self.gridLayoutWidget_2)
        self.gridLayout_2.setContentsMargins(0, 0, 0, 0)
        self.gridLayout_2.setObjectName("gridLayout_2")
        self.AnswerBox_2_1 = QtWidgets.QCheckBox(self.gridLayoutWidget_2)
        self.AnswerBox_2_1.setObjectName("AnswerBox_2_1")
        self.gridLayout_2.addWidget(self.AnswerBox_2_1, 0, 0, 1, 1)
        self.AnswerBox_2_3 = QtWidgets.QCheckBox(self.gridLayoutWidget_2)
        self.AnswerBox_2_3.setObjectName("AnswerBox_2_3")
        self.gridLayout_2.addWidget(self.AnswerBox_2_3, 2, 0, 1, 1)
        self.AnswerBox_2_2 = QtWidgets.QCheckBox(self.gridLayoutWidget_2)
        self.AnswerBox_2_2.setObjectName("AnswerBox_2_2")
        self.gridLayout_2.addWidget(self.AnswerBox_2_2, 1, 0, 1, 1)
        self.AnswerBox_2_4 = QtWidgets.QCheckBox(self.gridLayoutWidget_2)
        self.AnswerBox_2_4.setObjectName("AnswerBox_2_4")
        self.gridLayout_2.addWidget(self.AnswerBox_2_4, 3, 0, 1, 1)
        self.QuestionLabel_2 = QtWidgets.QLabel(self.centralwidget)
        self.QuestionLabel_2.setGeometry(QtCore.QRect(350, 110, 191, 41))
        self.QuestionLabel_2.setAlignment(QtCore.Qt.AlignCenter)
        self.QuestionLabel_2.setObjectName("QuestionLabel_2")
        self.AnswerLabel_2 = QtWidgets.QLabel(self.centralwidget)
        self.AnswerLabel_2.setGeometry(QtCore.QRect(550, 200, 121, 41))
        font = QtGui.QFont()
        font.setFamily("Arial")
        self.AnswerLabel_2.setFont(font)
        self.AnswerLabel_2.setText("")
        self.AnswerLabel_2.setAlignment(QtCore.Qt.AlignCenter)
        self.AnswerLabel_2.setObjectName("AnswerLabel_2")
        self.ContentsButton = QtWidgets.QPushButton(self.centralwidget)
        self.ContentsButton.setGeometry(QtCore.QRect(480, 360, 141, 41))
        font = QtGui.QFont()
        font.setUnderline(True)
        self.ContentsButton.setFont(font)
        self.ContentsButton.setObjectName("ContentsButton")
        TaskWindow_1.setCentralWidget(self.centralwidget)
        self.menubar = QtWidgets.QMenuBar(TaskWindow_1)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 689, 21))
        self.menubar.setObjectName("menubar")
        TaskWindow_1.setMenuBar(self.menubar)
        self.statusbar = QtWidgets.QStatusBar(TaskWindow_1)
        self.statusbar.setObjectName("statusbar")
        TaskWindow_1.setStatusBar(self.statusbar)
        self.retranslateUi(TaskWindow_1)
        QtCore.QMetaObject.connectSlotsByName(TaskWindow_1)

    def retranslateUi(self, TaskWindow_1):
        _translate = QtCore.QCoreApplication.translate
        TaskWindow_1.setWindowTitle(_translate("TaskWindow_1", "MainWindow"))
        self.label.setText(_translate("TaskWindow_1", "Watch the Video and answer the  questions:"))
        self.VideoButton.setText(_translate("TaskWindow_1", "Open Video"))
        self.QuestionLabel_1.setText(_translate("TaskWindow_1", "Who was the main hero of the video?"))
        self.AnswerButton_1_2.setText(_translate("TaskWindow_1", "A girl"))
        self.AnswerButton_1_3.setText(_translate("TaskWindow_1", "A dog"))
        self.AnswerButton_1_1.setText(_translate("TaskWindow_1", "A boy"))
        self.AnswerBox_2_1.setText(_translate("TaskWindow_1", "The girl was doing sports"))
        self.AnswerBox_2_3.setText(_translate("TaskWindow_1", "The girl was sleeping"))
        self.AnswerBox_2_2.setText(_translate("TaskWindow_1", "The girl was wearing a dress"))
        self.AnswerBox_2_4.setText(_translate("TaskWindow_1", "The girls was wearing sport outfit"))
        self.QuestionLabel_2.setText(_translate("TaskWindow_1", "What was happening in the video?"))
        self.ContentsButton.setText(_translate("TaskWindow_1", "Go to contents"))

if __name__ == "__main__":
    import sys
    app = QtWidgets.QApplication(sys.argv)
    TaskWindow_1 = QtWidgets.QMainWindow()
    ui = Ui_TaskWindow_1()
    ui.setupUi(TaskWindow_1)
    TaskWindow_1.show()
    sys.exit(app.exec_())