PyQt + Matplotlib

[Axel_Erfurt]

You could integrate the NavigationToolbar as a (movable) QToolbar

import sys
import matplotlib
matplotlib.use('Qt5Agg')
 
from PyQt5 import QtCore, QtGui, QtWidgets
 
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg, NavigationToolbar2QT as NavigationToolbar
from matplotlib.figure import Figure
 
 
class MplCanvas(FigureCanvasQTAgg):
 
    def __init__(self, parent=None, width=5, height=4, dpi=100):
        fig = Figure(figsize=(width, height), dpi=dpi)
        self.axes = fig.add_subplot(111)
        super(MplCanvas, self).__init__(fig)
 
 
class MainWindow(QtWidgets.QMainWindow):
 
    def __init__(self, *args, **kwargs):
        super(MainWindow, self).__init__(*args, **kwargs)
        
        sc = MplCanvas(self, width=5, height=4, dpi=100)
        sc.axes.plot([0,1,2,3,4], [10,1,20,3,40])
 
        # Create toolbar, passing canvas as first parament, parent (self, the MainWindow) as second.
        
        self.t_bar = self.addToolBar("File")
        self.t_bar.setContextMenuPolicy(QtCore.Qt.PreventContextMenu)
        self.t_bar.setMovable(False)
        self.t_bar.setAllowedAreas(QtCore.Qt.TopToolBarArea)
        
        self.action_one  = QtWidgets.QAction(self.style().standardIcon(QtWidgets.QStyle.SP_DirOpenIcon), 
                                        "One", triggered = self.on_action_one)
        self.t_bar.addAction(self.action_one)
        
        self.action_two  = QtWidgets.QAction(self.style().standardIcon(QtWidgets.QStyle.SP_DriveNetIcon), 
                                        "Two", triggered = self.on_action_two)
        self.t_bar.addAction(self.action_two)
        
        self.addToolBarBreak()
        
        self.sc_bar = self.addToolBar("SC")
        self.sc_bar.addWidget(NavigationToolbar(sc, None))
         
        layout = QtWidgets.QVBoxLayout()
        layout.addWidget(sc)
 
        # Create a placeholder widget to hold our toolbar and canvas.
        widget = QtWidgets.QWidget()
        widget.setLayout(layout)
        self.setCentralWidget(widget)
 
        self.show()
        
    def on_action_one(self):
        print("on_action_one")

    def on_action_two(self):
        print("on_action_two")
        
 
app = QtWidgets.QApplication(sys.argv)
w = MainWindow()
app.exec_()